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BASIC HYPERGEOMETRIC-SERIES

  • Basic hypergeometric series
  • Q-analog of hypergeometric series

    mathematics, basic hypergeometric series, or q-hypergeometric series, are q-analogue generalizations of generalized hypergeometric series, and are in turn

    Basic hypergeometric series

    Basic_hypergeometric_series

  • Elliptic hypergeometric series
  • Elliptic analog of hypergeometric series

    hypergeometric series where the ratio is a rational function of n, and basic hypergeometric series where the ratio is a periodic function of the complex number

    Elliptic hypergeometric series

    Elliptic_hypergeometric_series

  • Hypergeometric function
  • Function defined by a hypergeometric series

    the Gaussian or ordinary hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other

    Hypergeometric function

    Hypergeometric function

    Hypergeometric_function

  • Generalized hypergeometric function
  • Family of power series in mathematics

    generalized hypergeometric series is a power series in which the ratio of successive coefficients indexed by n is a rational function of n. The series, if convergent

    Generalized hypergeometric function

    Generalized hypergeometric function

    Generalized_hypergeometric_function

  • Series (mathematics)
  • Infinite sum

    {z^{n}}{n!}}} and their generalizations (such as basic hypergeometric series and elliptic hypergeometric series) frequently appear in integrable systems and

    Series (mathematics)

    Series_(mathematics)

  • Mizan Rahman
  • Bangladeshi Canadian mathematician and writer (1932–2015)

    scientific skepticism, freethinking and rationalism. He co-authored Basic Hypergeometric Series with George Gasper. This book is widely considered as the standard

    Mizan Rahman

    Mizan Rahman

    Mizan_Rahman

  • Barnes integral
  • Contour integral involving a product of gamma functions

    William Barnes (1908, 1910). They are closely related to generalized hypergeometric series. The integral is usually taken along a contour which is a deformation

    Barnes integral

    Barnes_integral

  • Eduard Heine
  • German mathematician (1821–1881)

    functions (Handbuch der Kugelfunctionen). He also investigated basic hypergeometric series. He introduced the Mehler–Heine formula. Heinrich Eduard Heine

    Eduard Heine

    Eduard Heine

    Eduard_Heine

  • Quantum calculus
  • Branch of mathematics

    geometry Quantum differential calculus Time scale calculus q-analog Basic hypergeometric series Quantum dilogarithm Abreu, Luis Daniel (2006). "Functions q-Orthogonal

    Quantum calculus

    Quantum_calculus

  • Q-Pochhammer symbol
  • Concept in combinatorics (part of mathematics)

    theory of basic hypergeometric series, it plays the role that the ordinary Pochhammer symbol plays in the theory of generalized hypergeometric series. Unlike

    Q-Pochhammer symbol

    Q-Pochhammer_symbol

  • George Gasper
  • American mathematician

    polynomials and basic hypergeometric series, who introduced the Askey–Gasper inequality. Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia

    George Gasper

    George_Gasper

  • Q-exponential
  • Q-analog in combinatorial mathematics

    z ) . {\displaystyle E_{q}(z).} It is a special case of the basic hypergeometric series, E q ( z ) = 1 ϕ 1 ( 0 0 ; z ) = ∑ n = 0 ∞ q ( n 2 ) ( − z )

    Q-exponential

    Q-exponential

  • Q-analog
  • Type of mathematical generalization

    known results. The earliest q-analog studied in detail is the basic hypergeometric series, which was introduced in the 19th century. q-analogs are most

    Q-analog

    Q-analog

  • Mock modular form
  • Complex-differentiable part of a Maass wave function

    Bringmann and Ken Ono showed that certain q-series arising from the Rogers–Fine basic hypergeometric series are related to holomorphic parts of weight

    Mock modular form

    Mock_modular_form

  • Nathan Fine
  • American mathematician (1916–1994)

    Beach, Florida) was an American mathematician who worked on basic hypergeometric series. He is best known for his lecture notes on the subject which

    Nathan Fine

    Nathan_Fine

  • Ramanujan theta function
  • Mathematical function

    Cambridge University Press. Gasper, George; Rahman, Mizan (2004). Basic Hypergeometric Series. Encyclopedia of Mathematics and Its Applications. Vol. 96 (2nd ed

    Ramanujan theta function

    Ramanujan_theta_function

  • List of q-analogs
  • distribution q-Weibull distribution Tsallis q-Gaussian Tsallis entropy Basic hypergeometric series Elliptic gamma function Hahn–Exton q-Bessel function Jackson

    List of q-analogs

    List_of_q-analogs

  • Continuous q-Laguerre polynomials
  • continuous q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous q-Laguerre polynomials

    Continuous_q-Laguerre_polynomials

  • Capacitance
  • Ability of a body to store an electrical charge

    119–120. doi:10.1093/imamat/34.1.119. Gasper; Rahman (2004). Basic Hypergeometric Series. Cambridge University Press. p. 20-22. ISBN 978-0-521-83357-8

    Capacitance

    Capacitance

    Capacitance

  • Rogers–Ramanujan identities
  • Mathematical identities related to integer partitions

    the Rogers–Ramanujan identities are two identities related to basic hypergeometric series and integer partitions. The identities were first discovered

    Rogers–Ramanujan identities

    Rogers–Ramanujan_identities

  • F. H. Jackson
  • British mathematician

    1960) was an English clergyman and mathematician who worked on basic hypergeometric series. He introduced several q-analogs such as the Jackson–Bessel functions

    F. H. Jackson

    F._H._Jackson

  • Summation by parts
  • Theorem to simplify sums of products of sequences

    Chu, Wenchang (2007). "Abel's lemma on summation by parts and basic hypergeometric series". Advances in Applied Mathematics. 39 (4): 490–514. doi:10.1016/j

    Summation by parts

    Summation_by_parts

  • Continuous q-Hermite polynomials
  • continuous q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous q-Hermite polynomials

    Continuous_q-Hermite_polynomials

  • Appell series
  • Set of four hypergeometric series

    In mathematics, Appell series are a set of four hypergeometric series F1, F2, F3, F4 of two variables that were introduced by Paul Appell (1880) and that

    Appell series

    Appell_series

  • Continuous big q-Hermite polynomials
  • Family of basic hypergeometric orthogonal polynomials

    continuous big q-Hermite polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous big q-Hermite polynomials

    Continuous_big_q-Hermite_polynomials

  • Wilfrid Norman Bailey
  • British mathematician

    introduced Bailey's lemma and Bailey pairs into the theory of basic hypergeometric series. Bailey chains and Bailey transforms are named after him. Slater

    Wilfrid Norman Bailey

    Wilfrid_Norman_Bailey

  • Askey scheme
  • Classification of orthogonal polynomials

    scheme is a way of organizing orthogonal polynomials of hypergeometric or basic hypergeometric type into a hierarchy. For the classical orthogonal polynomials

    Askey scheme

    Askey_scheme

  • Bilateral hypergeometric series
  • Mathematical series

    In mathematics, a bilateral hypergeometric series is a series Σan summed over all integers n, and such that the ratio an/an+1 of two terms is a rational

    Bilateral hypergeometric series

    Bilateral_hypergeometric_series

  • Big q-Laguerre polynomials
  • the big q-Laguerre polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Big q-Laguerre polynomials

    Big_q-Laguerre_polynomials

  • Quantum q-Krawtchouk polynomials
  • quantum q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Quantum q-Krawtchouk polynomials

    Quantum_q-Krawtchouk_polynomials

  • Q-Racah polynomials
  • mathematics, the q-Racah polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Askey & Wilson (1979)

    Q-Racah polynomials

    Q-Racah_polynomials

  • Q-Meixner–Pollaczek polynomials
  • q-Meixner–Pollaczek polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Q-Meixner–Pollaczek polynomials

    Q-Meixner–Pollaczek_polynomials

  • List of University of Dhaka alumni and faculty members
  • Alumni of university

    mathematician, author of the standard work of choice in the field of Basic Hypergeometric Series S.M. Ullah, soil scientist and environmentalist who researched

    List of University of Dhaka alumni and faculty members

    List_of_University_of_Dhaka_alumni_and_faculty_members

  • Q-gamma function
  • Function in q-analog theory

    ISSN 0950-1207, JSTOR 92601 Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 96 (2nd ed

    Q-gamma function

    Q-gamma_function

  • Q-Charlier polynomials
  • mathematics, the q-Charlier polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Q-Charlier polynomials

    Q-Charlier_polynomials

  • Continuous dual q-Hahn polynomials
  • continuous dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous dual q-Hahn polynomials

    Continuous_dual_q-Hahn_polynomials

  • Q-Hahn polynomials
  • mathematics, the q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Q-Hahn polynomials

    Q-Hahn_polynomials

  • Little q-Jacobi polynomials
  • Mathematical family

    q-Jacobi polynomials pn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Hahn (1949). Roelof

    Little q-Jacobi polynomials

    Little_q-Jacobi_polynomials

  • Affine q-Krawtchouk polynomials
  • affine q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Carlitz and Hodges

    Affine q-Krawtchouk polynomials

    Affine_q-Krawtchouk_polynomials

  • Q-Meixner polynomials
  • mathematics, the q-Meixner polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Q-Meixner polynomials

    Q-Meixner_polynomials

  • Dual q-Hahn polynomials
  • Family of hypergeometric orthogonal polynomials

    mathematics, the dual q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Dual q-Hahn polynomials

    Dual_q-Hahn_polynomials

  • Dual q-Krawtchouk polynomials
  • dual q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Dual q-Krawtchouk polynomials

    Dual_q-Krawtchouk_polynomials

  • Askey–Gasper inequality
  • give some generalizations of the Askey–Gasper inequality to basic hypergeometric series. Turán's inequalities Askey, Richard; Gasper, George (1976),

    Askey–Gasper inequality

    Askey–Gasper_inequality

  • Series acceleration
  • Mathematical technique for improving convergence

    applied to the hypergeometric series gives some of the classic, well-known hypergeometric series identities. Given an infinite series with a sequence

    Series acceleration

    Series_acceleration

  • Dixon's identity
  • On finite sums of products of three binomial coefficients, and a hypergeometric sum

    the Selberg integral. A q-analogue of Dixon's formula for the basic hypergeometric series in terms of the q-Pochhammer symbol is given by 4 φ 3 [ a − q

    Dixon's identity

    Dixon's_identity

  • Q-Laguerre polynomials
  • Stieltjes–Wigert polynomials P(α) n(x;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme introduced by Moak 1981. Koekoek,

    Q-Laguerre polynomials

    Q-Laguerre_polynomials

  • Continuous q-Jacobi polynomials
  • Family of orthogonal polynomials

    introduced by Askey & Wilson (1985), are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous q-Jacobi polynomials

    Continuous_q-Jacobi_polynomials

  • Jacobi polynomials
  • Polynomial sequence

    In mathematics, Jacobi polynomials (occasionally called hypergeometric polynomials) P n ( α , β ) ( x ) {\displaystyle P_{n}^{(\alpha ,\beta )}(x)} are

    Jacobi polynomials

    Jacobi polynomials

    Jacobi_polynomials

  • Little q-Laguerre polynomials
  • or Wall polynomials Wn(x; b,q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme closely related to a continued fraction

    Little q-Laguerre polynomials

    Little_q-Laguerre_polynomials

  • Q-Krawtchouk polynomials
  • the q-Krawtchouk polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme Roelof Koekoek, Peter A. Lesky, and

    Q-Krawtchouk polynomials

    Q-Krawtchouk_polynomials

  • Q-Bessel polynomials
  • mathematics, the q-Bessel polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Q-Bessel polynomials

    Q-Bessel_polynomials

  • Al-Salam–Chihara polynomials
  • Family of basic hypergeometric orthogonal polynomials in the basic Askey scheme

    Al-Salam–Chihara polynomials Qn(x;a,b;q) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Chihara (1976)

    Al-Salam–Chihara polynomials

    Al-Salam–Chihara_polynomials

  • Elliptic gamma function
  • Mathematic function

    ISSN 0950-1207, JSTOR 92601 Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 96 (2nd ed

    Elliptic gamma function

    Elliptic_gamma_function

  • Big q-Jacobi polynomials
  • family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. The polynomials are given in terms of basic hypergeometric functions

    Big q-Jacobi polynomials

    Big_q-Jacobi_polynomials

  • Continuous q-Hahn polynomials
  • Hypergeometric orthogonal polynomials

    continuous q-Hahn polynomials are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme. Roelof Koekoek, Peter A. Lesky, and

    Continuous q-Hahn polynomials

    Continuous_q-Hahn_polynomials

  • Jackson q-Bessel function
  • functions are given in terms of the q-Pochhammer symbol and the basic hypergeometric function ϕ {\displaystyle \phi } by J ν ( 1 ) ( x ; q ) = ( q ν +

    Jackson q-Bessel function

    Jackson_q-Bessel_function

  • Discrete q-Hermite polynomials
  • closely related families hn(x;q) and ĥn(x;q) of basic hypergeometric orthogonal polynomials in the basic Askey scheme, introduced by Al-Salam and Carlitz (1965)

    Discrete q-Hermite polynomials

    Discrete_q-Hermite_polynomials

  • Clausen's formula
  • Mathematical formula by Thomas Clausen

    Clausen (1828), expresses the square of a Gaussian hypergeometric series as a generalized hypergeometric series. It states 2 F 1 [ a b a + b + 1 / 2 ; x ] 2

    Clausen's formula

    Clausen's_formula

  • Rogers polynomials
  • Family of orthogonal polynomials

    polynomials can be defined in terms of the q-Pochhammer symbol and the basic hypergeometric series by C n ( x ; β | q ) = ( β ; q ) n ( q ; q ) n e i n θ 2 ϕ 1

    Rogers polynomials

    Rogers_polynomials

  • Q-theta function
  • elliptic hypergeometric series Jacobi theta function Ramanujan theta function Gasper, George; Rahman, Mizan (2004). Basic Hypergeometric Series. doi:10

    Q-theta function

    Q-theta_function

  • Big q-Legendre polynomials
  • orthogonal family of polynomials defined in terms of Heine's basic hypergeometric series as P n ( x ; c ; q ) = 3 ϕ 2 ( q − n , q n + 1 , x ; q , c q

    Big q-Legendre polynomials

    Big_q-Legendre_polynomials

  • Rogers–Szegő polynomials
  • (3). doi:10.37236/2481. Gasper, George; Rahman, Mizan (2004), Basic hypergeometric series, Encyclopedia of Mathematics and its Applications, vol. 96 (2nd ed

    Rogers–Szegő polynomials

    Rogers–Szegő_polynomials

  • Stieltjes–Wigert polynomials
  • Stieltjes and Carl Severin Wigert) are a family of basic hypergeometric orthogonal polynomials in the basic Askey scheme, for the weight function w ( x ) =

    Stieltjes–Wigert polynomials

    Stieltjes–Wigert_polynomials

  • Meijer G-function
  • Generalization of the hypergeometric function

    particular cases. This was not the only attempt of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's

    Meijer G-function

    Meijer G-function

    Meijer_G-function

  • Closed-form expression
  • Mathematical formula involving a given set of operations

    error function or gamma function to be basic. It is possible to solve the quintic equation if general hypergeometric functions are included, although the

    Closed-form expression

    Closed-form_expression

  • Askey–Wilson polynomials
  • }&ae^{-i\theta }\\ab&ac&ad\end{matrix}};q,q\right]} where φ is a basic hypergeometric function, x = cos θ, and (,,,)n is the q-Pochhammer symbol. Askey–Wilson

    Askey–Wilson polynomials

    Askey–Wilson_polynomials

  • Transcendental function
  • Analytic function that does not satisfy a polynomial equation

    arXiv:1004.1668v1 [math.NT]. Archinard, N. (2003). "Exceptional sets of hypergeometric series". Journal of Number Theory. 101 (2): 244–269. doi:10.1016/S0022-314X(03)00042-8

    Transcendental function

    Transcendental_function

  • Lucy Joan Slater
  • British mathematician (1922-2008)

    Slater (5 January 1922 – 6 June 2008) was a mathematician who worked on hypergeometric functions, and who found many generalizations of the Rogers–Ramanujan

    Lucy Joan Slater

    Lucy_Joan_Slater

  • Nayandeep Deka Baruah
  • Indian mathematician and professor (born 1972)

    papers so far related to special functions, modular equation, Basic hypergeometric series and integer partitions.[better source needed] He has so far guided

    Nayandeep Deka Baruah

    Nayandeep Deka Baruah

    Nayandeep_Deka_Baruah

  • List of mathematical functions
  • Kummer's function Riesz function Hypergeometric functions: Versatile family of power series. Confluent hypergeometric function Associated Legendre functions

    List of mathematical functions

    List_of_mathematical_functions

  • Alexander Varchenko
  • of Order Four (University Lecture Series), AMS 1992, ISBN 0821870025 Varchenko, A. Multidimensional hypergeometric functions and representation theory

    Alexander Varchenko

    Alexander Varchenko

    Alexander_Varchenko

  • Richard Askey
  • American mathematician (1933–2019)

    ISBN 978-0-89871-018-2, MR 0481145. Richard Askey; James Wilson (1985), "Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials", Memoirs

    Richard Askey

    Richard Askey

    Richard_Askey

  • Combinatorics
  • Branch of discrete mathematics

    extended to an infinite (specifically, countable) but discrete setting. Basic combinatorial concepts and enumerative results appeared throughout the ancient

    Combinatorics

    Combinatorics

  • SymPy
  • Python library for symbolic computation

    hypergeometric, special functions, etc. Substitution Arbitrary precision integers, rationals and floats Noncommutative symbols Pattern matching Basic

    SymPy

    SymPy

    SymPy

  • Spherical harmonics
  • Special mathematical functions defined on the surface of a sphere

    is given by the hypergeometric series; furthermore, the spherical harmonics can be re-expressed in terms of the hypergeometric series, as SO(3) = PSU(2)

    Spherical harmonics

    Spherical harmonics

    Spherical_harmonics

  • Carl Friedrich Gauss
  • German polymath and scholar (1777–1855)

    theory of binary and ternary quadratic forms, and the theory of hypergeometric series. When Gauss was only 19 years old, he proved the construction of

    Carl Friedrich Gauss

    Carl Friedrich Gauss

    Carl_Friedrich_Gauss

  • Generating function
  • Formal power series

    function Li2(z), the generalized hypergeometric functions pFq(...; ...; z) and the functions defined by the power series ∑ n = 0 ∞ z n ( n ! ) 2 {\displaystyle

    Generating function

    Generating_function

  • Outline of probability
  • Overview of and topical guide to probability

    binomial, negative binomial, (discrete) uniform, geometric, Poisson, and hypergeometric. Continuous: (continuous) uniform, exponential, gamma, beta, normal

    Outline of probability

    Outline_of_probability

  • Incomplete gamma function
  • Types of special mathematical functions

    {z^{s+k}}{s+k}}={\frac {z^{s}}{s}}M(s,s+1,-z),} where M is Kummer's confluent hypergeometric function. When the real part of z is positive, γ ( s , z ) = s − 1 z

    Incomplete gamma function

    Incomplete gamma function

    Incomplete_gamma_function

  • Simple random sample
  • Sampling technique

    distribution. For a simple random sample without replacement, one obtains a hypergeometric distribution. Several efficient algorithms for simple random sampling

    Simple random sample

    Simple_random_sample

  • Inverse trigonometric functions
  • Inverse functions of sin, cos, tan, etc.

    Euler, the second by Carl Friedrich Gauss utilizing the Gaussian hypergeometric series. For real and complex values of z: ∫ arcsin ⁡ ( z ) d z = z arcsin

    Inverse trigonometric functions

    Inverse trigonometric functions

    Inverse_trigonometric_functions

  • Hahn–Exton q-Bessel function
  • }{}_{1}\phi _{1}(0;q^{\nu +1};q,qx^{2}).} ϕ {\displaystyle \phi } is the basic hypergeometric function. Koelink and Swarttouw proved that J ν ( 3 ) ( x ; q ) {\displaystyle

    Hahn–Exton q-Bessel function

    Hahn–Exton_q-Bessel_function

  • Error function
  • Sigmoid shape special function

    the Mittag-Leffler function, and can also be expressed as a confluent hypergeometric function (Kummer's function): erf ⁡ ( x ) = 2 x π M ( 1 2 , 3 2 , −

    Error function

    Error function

    Error_function

  • Euler's constant
  • Difference between logarithm and harmonic series

    2024-11-01. "DLMF: §13.2 Definitions and Basic Properties ‣ Kummer Functions ‣ Chapter 11 Confluent Hypergeometric Functions". dlmf.nist.gov. Retrieved 2024-11-01

    Euler's constant

    Euler's constant

    Euler's_constant

  • Binomial distribution
  • Probability distribution

    the draws are not independent and so the resulting distribution is a hypergeometric distribution, not a binomial one. However, for N much larger than n

    Binomial distribution

    Binomial distribution

    Binomial_distribution

  • Computer algebra
  • Scientific area at the interface between computer science and mathematics

    F5 algorithm) Gosper's algorithm: find sums of hypergeometric terms that are themselves hypergeometric terms Knuth–Bendix completion algorithm: for rewriting

    Computer algebra

    Computer algebra

    Computer_algebra

  • Exponential function
  • Mathematical function, denoted exp(x) or e^x

    e k x = ( e k ) x = b x . {\displaystyle e^{kx}=(e^{k})^{x}=b^{x}.} The basic properties of the exponential function (derivative and functional equation)

    Exponential function

    Exponential function

    Exponential_function

  • Pearson correlation coefficient
  • Measure of linear correlation

    z ) {\displaystyle {}_{2}\mathrm {F} _{1}(a,b;c;z)} is the Gaussian hypergeometric function. In the special case when ρ = 0 {\displaystyle \rho =0} (zero

    Pearson correlation coefficient

    Pearson correlation coefficient

    Pearson_correlation_coefficient

  • Lerch transcendent
  • Special mathematical function

    (Includes various basic identities in the introduction.) Jackson, M. (1950), "On Lerch's transcendent and the basic bilateral hypergeometric series 2ψ2", J. London

    Lerch transcendent

    Lerch_transcendent

  • Beta distribution
  • Probability distribution

    characteristic function of the beta distribution is Kummer's confluent hypergeometric function (of the first kind): φ X ( α ; β ; t ) = E ⁡ [ e i t X ] =

    Beta distribution

    Beta distribution

    Beta_distribution

  • Method of steepest descent
  • Extension of Laplace's method for approximating integrals

    out that it occurred in the unpublished note by Riemann (1863) about hypergeometric functions. The contour of steepest descent has a minimax property, see

    Method of steepest descent

    Method_of_steepest_descent

  • Probability distribution
  • Mathematical function for the probability a given outcome occurs in an experiment

    hypergeometric distribution, similar to the multinomial distribution, but using sampling without replacement; a generalization of the hypergeometric distribution

    Probability distribution

    Probability distribution

    Probability_distribution

  • Automorphic form
  • Type of generalization of periodic functions in Euclidean space

    existence of a class of Fuchsian functions, those which come from the hypergeometric series; I had only to write out the results, which took but a few hours

    Automorphic form

    Automorphic_form

  • Jackson integral
  • integrals", Q. J. Pure Appl. Math. 41 193–203. Exton, Harold (1983). Q-hypergeometric functions and applications. Chichester [West Sussex]: E. Horwood. ISBN 978-0470274538

    Jackson integral

    Jackson_integral

  • Integral
  • Operation in mathematical calculus

    antiderivatives, the special functions (like the Legendre functions, the hypergeometric function, the gamma function, the incomplete gamma function and so on)

    Integral

    Integral

    Integral

  • Normal distribution
  • Probability distribution

    the plain and absolute moments can be expressed in terms of confluent hypergeometric functions 1 F 1 {\textstyle {}_{1}F_{1}} and U . {\textstyle U.} E ⁡

    Normal distribution

    Normal distribution

    Normal_distribution

  • Zernike polynomials
  • Polynomial sequence

    {n-2k}{{\tfrac {n-m}{2}}-k}}\rho ^{n-2k}} . A notation as terminating Gaussian hypergeometric functions is useful to reveal recurrences, to demonstrate that they

    Zernike polynomials

    Zernike polynomials

    Zernike_polynomials

  • Special functions
  • Mathematical functions having established names and notations

    theory of orthogonal polynomials is of a definite but limited scope. Hypergeometric series, observed by Felix Klein to be important in astronomy and mathematical

    Special functions

    Special_functions

  • Clausen function
  • Transcendental single-variable function

    hypergeometric series, summations involving the inverse of the central binomial coefficient, sums of the polygamma function, and Dirichlet L-series.

    Clausen function

    Clausen function

    Clausen_function

  • Bateman Manuscript Project
  • (editors: Tom H. Koornwinder, Jasper V. Stokman) Volume 3: Hypergeometric and Basic Hypergeometric Functions (editor: Mourad Ismail) Further volumes were

    Bateman Manuscript Project

    Bateman_Manuscript_Project

AI & ChatGPT searchs for online references containing BASIC HYPERGEOMETRIC-SERIES

BASIC HYPERGEOMETRIC-SERIES

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BASIC HYPERGEOMETRIC-SERIES

  • Basir
  • Boy/Male

    Indian

    Basir

    Vision, Propitious, Auspicious, Prudent, Bringer of glad tidings

    Basir

  • Basil
  • Boy/Male

    Greek American English

    Basil

    Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....

    Basil

  • Basil |
  • Boy/Male

    Muslim

    Basil |

    King, Basil the herb (1)

    Basil |

  • Basic
  • Boy/Male

    Greek

    Basic

    Royal. Kingly. St Basil the Great was Bishop of Caesarea in the latter half of the 4th century....

    Basic

  • Basir |
  • Boy/Male

    Muslim

    Basir |

    Vision, Propitious, Auspicious, Prudent, Bringer of glad tidings

    Basir |

  • Basit |
  • Boy/Male

    Muslim

    Basit |

    Vast, Spacious, One who stretches, Enlarges

    Basit |

  • Neev
  • Boy/Male

    Hindu

    Neev

    Basic, Foundation

    Neev

  • Basir
  • Boy/Male

    Turkish

    Basir

    Intelligent.

    Basir

  • BASIA
  • Female

    Hebrew

    BASIA

     Variant spelling of Hebrew Basya, BASIA means "daughter of God."

    BASIA

  • Basil
  • Boy/Male

    Hindu

    Basil

    King, Basil the herb

    Basil

  • Niv
  • Boy/Male

    Hindu

    Niv

    Basic, Foundation

    Niv

  • Niv | நீவ
  • Boy/Male

    Tamil

    Niv | நீவ

    Basic, Foundation

    Niv | நீவ

  • Basiq |
  • Boy/Male

    Muslim

    Basiq |

    Clear

    Basiq |

  • Basil
  • Surname or Lastname

    English and French

    Basil

    English and French : from a medieval personal name, ultimately from Greek Basileios ‘royal’. The name was borne by a 4th-century bishop of Caesarea in Cappadocia, regarded as one of the four Fathers of the Eastern Church; he wrote important theological works and established a rule for religious orders of monks. Various other saints are also known under these and cognate names. The popularity of Vasili as a Russian personal name is largely due to the fact that this was the ecclesiastical name of St. Vladimir (956–1015), Prince of Kiev, who was chiefly responsible for the introduction of Christianity to Russia. As an American surname, this has also absorbed some Greek, Russian, and other derivatives of Greek Vasili.

    Basil

  • Basit
  • Boy/Male

    Indian

    Basit

    Vast, Spacious, One who stretches, Enlarges

    Basit

  • Neev | நீவ 
  • Boy/Male

    Tamil

    Neev | நீவ 

    Basic, Foundation

    Neev | நீவ 

  • BASIL
  • Male

    English

    BASIL

     English form of French Basile, BASIL means "king." Also sometimes given as an herb name.

    BASIL

  • Basim |
  • Boy/Male

    Muslim

    Basim |

    Smiling, Happy

    Basim |

  • Basim
  • Boy/Male

    Indian

    Basim

    Smiling, Happy

    Basim

  • Basil | பஸில
  • Boy/Male

    Tamil

    Basil | பஸில

    King, Basil the herb

    Basil | பஸில

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Online names & meanings

  • Isheeta | ஈஷிதா
  • Girl/Female

    Tamil

    Isheeta | ஈஷிதா

    Mastery, Wealth, Superior

  • Noriza |
  • Girl/Female

    Muslim

    Noriza |

    Light of contentment

  • Jumah
  • Boy/Male

    African, Arabic, Hindu, Indian, Muslim

    Jumah

    Born on Friday

  • Jaffer
  • Boy/Male

    Arabic, Australian, Muslim

    Jaffer

    Stream

  • Niru
  • Girl/Female

    Assamese, Hindu, Indian

    Niru

    Water

  • Kobinath | கோபீநாத
  • Boy/Male

    Tamil

    Kobinath | கோபீநாத

  • Whitlow
  • Surname or Lastname

    English

    Whitlow

    English : variant of Whitelaw.

  • Jahangir
  • Boy/Male

    Muslim/Islamic

    Jahangir

    A moghul emperor had this name

  • Prekshith
  • Boy/Male

    Hindu, Indian

    Prekshith

    Inspire

  • Rahitya
  • Girl/Female

    Hindu, Indian

    Rahitya

    Inviting Goddess Laxmi

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BASIC HYPERGEOMETRIC-SERIES

Top AI & ChatGPT search, Social media, medium, facebook & news articles containing BASIC HYPERGEOMETRIC-SERIES

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Other words and meanings similar to

BASIC HYPERGEOMETRIC-SERIES

AI search in online dictionary sources & meanings containing BASIC HYPERGEOMETRIC-SERIES

BASIC HYPERGEOMETRIC-SERIES

  • Firmament
  • v. & a.

    Fixed foundation; established basis.

  • Basic
  • a.

    Having the base in excess, or the amount of the base atomically greater than that of the acid, or exceeding in proportion that of the related neutral salt.

  • Basiled
  • imp. & p. p.

    of Basil

  • Basiling
  • p. pr. & vb. n.

    of Basil

  • Subsalt
  • n.

    A basic salt. See the Note under Salt.

  • Basic
  • a.

    Apparently alkaline, as certain normal salts which exhibit alkaline reactions with test paper.

  • Basined
  • a.

    Inclosed in a basin.

  • Phloramine
  • n.

    A basic amido derivative of phloroglucin, having an astringent taste.

  • Electro-negative
  • a.

    Negative; nonmetallic; acid; -- opposed to positive, metallic, or basic.

  • Zincous
  • a.

    Hence, formerly, basic, basylous, as opposed to chlorous.

  • Subsilicate
  • n.

    A basic silicate.

  • Basic
  • a.

    Relating to a base; performing the office of a base in a salt.

  • Acidic
  • a.

    Containing a high percentage of silica; -- opposed to basic.

  • Bason
  • n.

    A basin.

  • Basin
  • n.

    The quantity contained in a basin.

  • Basic
  • a.

    Said of crystalline rocks which contain a relatively low percentage of silica, as basalt.

  • Bases
  • pl.

    of Basis

  • Positive
  • a.

    Hence, basic; metallic; not acid; -- opposed to negative, and said of metals, bases, and basic radicals.

  • Baric
  • a.

    Of or pertaining to barium; as, baric oxide.

  • Basil
  • n.

    The name given to several aromatic herbs of the Mint family, but chiefly to the common or sweet basil (Ocymum basilicum), and the bush basil, or lesser basil (O. minimum), the leaves of which are used in cookery. The name is also given to several kinds of mountain mint (Pycnanthemum).