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Solution of a confluent hypergeometric equation
mathematics, a confluent hypergeometric function is a solution of a confluent hypergeometric equation, which is a degenerate form of a hypergeometric differential
Confluent hypergeometric function
Confluent_hypergeometric_function
Family of power series in mathematics
(Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special
Generalized hypergeometric function
Generalized_hypergeometric_function
Function defined by a hypergeometric series
ordinary hypergeometric function 2F1(a, b; c; z) is a special function represented by the hypergeometric series, that includes many other special functions as
Hypergeometric_function
Sigmoid shape special function
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 , − x 2 ) . {\displaystyle
Error_function
Concept in mathematics
; z ) {\displaystyle \;_{1}F_{1}(a;b;z)=M(a;b;z)} is the confluent hypergeometric function. Other pairs of independent solutions may be formed from linear
Parabolic_cylinder_function
Generalization of the hypergeometric function
of its kind: the generalized hypergeometric function and the MacRobert E-function had the same aim, but Meijer's G-function was able to include those as
Meijer_G-function
In physics, solution to Schrödinger equation
Coulomb potential and can be written in terms of confluent hypergeometric functions or Whittaker functions of imaginary argument. The Coulomb wave equation
Coulomb_wave_function
In mathematics, a solution to a modified form of the confluent hypergeometric equation
mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by
Whittaker_function
Polynomial sequence
Confluent hypergeometric functions of the first kind. The conventional Hermite polynomials may also be expressed in terms of confluent hypergeometric
Hermite_polynomials
Multivalued function in mathematics
stationary one-dimensional Schrödinger equation in terms of the confluent hypergeometric functions. The potential is given as V = V 0 1 + W ( e − x σ ) . {\displaystyle
Lambert_W_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
Incomplete_gamma_function
Special function defined by an integral
connexion with the confluent hypergeometric functions is that E 1 {\displaystyle E_{1}} is an exponential times the function U ( 1 , 1 , z ) {\displaystyle
Exponential_integral
function Riesz function Hypergeometric functions: Versatile family of power series. Confluent hypergeometric function Associated Legendre functions Meijer G-function
List of mathematical functions
List_of_mathematical_functions
Sequence of differential equation solutions
{1}{(1-t)^{\alpha +1}}}e^{-tx/(1-t)}.} Laguerre functions are defined by confluent hypergeometric functions and Kummer's transformation as L n ( α ) ( x
Laguerre_polynomials
Probability distribution
where 1F1 is the confluent hypergeometric function and J1 is the Bessel function of the first kind. Likewise the moment generating function can be calculated
Wigner semicircle distribution
Wigner_semicircle_distribution
In mathematics, the Bateman function (or k-function) is a special case of the confluent hypergeometric function studied by Harry Bateman(1931). Bateman
Bateman_function
Probability distribution
characteristic function of the beta distribution to a Bessel function, since in the special case α + β = 2α the confluent hypergeometric function (of the first
Beta_distribution
Concept in probability theory and statistics
theory and statistics, the moment generating function of a real-valued random variable is a generating function that provides an alternative specification
Moment_generating_function
Monochrome light beam whose amplitude envelope is a Gaussian function
real-valued, Γ(x) is the gamma function and 1F1(a, b; x) is a confluent hypergeometric function. Some subfamilies of hypergeometric-Gaussian (HyGG) modes can
Gaussian_beam
Special function defined by an integral
{i^{k}}{(m+nk+1)}}{\frac {x^{m+nk+1}}{k!}}} is a confluent hypergeometric function and also an incomplete gamma function ∫ x m e i x n d x = x m + 1 m + 1 1 F 1
Fresnel_integral
Mathematical function
mathematics, there are several functions known as Kummer's function. One is known as the confluent hypergeometric function of Kummer. Another one, defined
Kummer's_function
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
Set of four hypergeometric series
which generalize Kummer's confluent hypergeometric function 1F1 of one variable and the confluent hypergeometric limit function 0F1 of one variable in a
Appell_series
Probability distribution
b ; z ) {\displaystyle M(a,b,z)=_{1}F_{1}(a;b;z)} is the confluent hypergeometric function of the first kind. When k {\displaystyle k} is even, the
Rice_distribution
Difference between logarithm and harmonic series
Kummer Functions ‣ Chapter 11 Confluent Hypergeometric Functions". dlmf.nist.gov. Retrieved 2024-11-01. "DLMF: §9.12 Scorer Functions ‣ Related Functions ‣
Euler's_constant
Function for Heun's differential equation
symmetries of the hypergeometric differential equations obtained by Kummer.[citation needed] The symmetries fixing the local Heun function form a group of
Heun_function
Topics referred to by the same term
Confluence Project, a web-based volunteer project Confluent hypergeometric function, a mathematical function Confluent, a data streaming software company Convergence
Confluence_(disambiguation)
Mathematics concept
{1}{2}}}(1/x)} The Bessel polynomial may also be defined as a confluent hypergeometric function y n ( x ) = 2 F 0 ( − n , n + 1 ; ; − x / 2 ) = ( 2 x ) −
Bessel_polynomials
Continuous probability distribution
where U ( a , b , z ) {\displaystyle U(a,b,z)} is the confluent hypergeometric function of the second kind. In instances where the F-distribution
F-distribution
here by Cunningham (1908). It can be defined in terms of the confluent hypergeometric function U, by ω m , n ( x ) = e − x + π i ( m / 2 − n ) Γ ( 1 + n
Cunningham_function
Probability distribution
, z ) {\displaystyle M(a,b,z)} is Kummer's confluent hypergeometric function. The characteristic function is given by: φ ( t ; k ) = M ( k 2 , 1 2 , −
Chi_distribution
Probability distribution
parameter μ can be expressed in several forms. The confluent hypergeometric function form of the density function is f ( x ) = Γ ( ν + 1 2 ) ν π Γ ( ν 2 ) ( 1
Noncentral_t-distribution
Horn function classification scheme. The total 34 Horn functions can be further categorised into 14 complete hypergeometric functions and 20 confluent hypergeometric
Horn_function
British mathematician and historian of science (1873–1956)
Whittaker is the eponym of the Whittaker function or Whittaker integral, in the theory of confluent hypergeometric functions. This makes him also the eponym of
E._T._Whittaker
In mathematics, the Toronto function T(m,n,r) is a modification of the confluent hypergeometric function defined by Heatley (1943), Weisstein, as T ( m
Toronto_function
Geometric shape
data than any one segment of a 3rd order curve. B-spline Confluent hypergeometric function Eugene V. Shikin; Alexander I. Plis (14 July 1995). Handbook
Composite_Bézier_curve
confluent hypergeometric series 1F1 of one variable and the confluent hypergeometric limit function 0F1 of one variable. The first of these double series was
Humbert_series
Document that proposed additions to the C++ standard library
file: Polymorphic function wrapper (function) – can store any callable function (function pointers, member function pointers, and function objects) that uses
C++_Technical_Report_1
American mathematician (1942–2010)
was a major contributor to the field of special functions, especially confluent hypergeometric functions. A native of Brooklyn, New York, Miller attended
Allen_R._Miller
Probability distribution
distribution has also been expressed with Kummer's confluent hypergeometric function or the Hermite function. This was shown in Springer.. A transformation
Ratio_distribution
Ansatz in condensed matter physics
M {\displaystyle M} is a confluent hypergeometric function and J 0 {\displaystyle {\mathcal {J}}_{0}} is a Bessel function of the first kind. Here, r
Laughlin_wavefunction
British mathematician (1922-2008)
(1960), Confluent hypergeometric functions, Cambridge, UK: Cambridge University Press, MR 0107026 Slater, Lucy Joan (1966), Generalized hypergeometric functions
Lucy_Joan_Slater
Antipodally symmetric probability distribution on the n-sphere
) {\displaystyle {}_{1}F_{1}(\cdot ;\cdot ,\cdot )} is a confluent hypergeometric function of matrix argument. The matrices M and Z are the result of
Bingham_distribution
Probability distribution with more than one mode
deviation of 1. R has a known density that can be expressed as a confluent hypergeometric function. The distribution of the reciprocal of a t distributed random
Multimodal_distribution
Probability distribution in physics
{\tfrac {1}{2}}\chi ^{2})}}} where M(·,·,·) is the Kummer's confluent hypergeometric function.[circular reference] The variance is: σ 2 = c 2 ( χ 2 ) p
ARGUS_distribution
Mathematical lemma on asymptotic behavior of integrals
integral in question. When 0 < a < b {\displaystyle 0<a<b} , the confluent hypergeometric function of the first kind has the integral representation 1 F 1 (
Watson's_lemma
Table of integrals compiled by I. S. Gradshteyn and I. M. Ryzhik
integrals in Gradshteyn and Ryzhik. Part 28: The confluent hypergeometric function and Whittaker functions" (PDF). Scientia. Series A: Mathematical Sciences
Gradshteyn_and_Ryzhik
Textbook in mathematical analysis
Transcendental Functions The Gamma Function The Zeta Function of Riemann The Hypergeometric Function Legendre Functions The Confluent Hypergeometric Function Bessel
A_Course_of_Modern_Analysis
Term in the mathematical theory of special functions
zeros of the Laguerre polynomials, or equivalently, of the confluent hypergeometric function, defined as the finite (ordered) set ( ℓ h , j ( α , x ) )
Pochhammer_k-symbol
1964 mathematical reference work edited by M. Abramowitz and I. Stegun
Functions Confluent Hypergeometric Functions Coulomb Wave Functions Hypergeometric Functions Jacobian Elliptic Functions and Theta Functions Elliptic Integrals
Abramowitz_and_Stegun
Probability distribution
probability mass function, \alpha=m/2 and \beta=n/2 are shape parameters, and I x ( a , b ) {\displaystyle I_{x}(a,b)} is the incomplete beta function. That is
Noncentral_beta_distribution
} Here, M is a confluent hypergeometric function. For an application of this integral see Charge density spread over a wave function. Relation between
Common integrals in quantum field theory
Common_integrals_in_quantum_field_theory
Lucy Joan (1968). "Confluent Hypergeometric Function". In Abramowitz, Milton; Stegun, Irene (eds.). Handbook of Mathematical Functions. New York: Dover
Beta_wavelet
Formula describing the asymptotic behavior of the Legendre polynomials
} where Jα is the Bessel function of order α. Using generalized Laguerre polynomials and confluent hypergeometric functions, they can be written as lim
Mehler–Heine_formula
and major contributor to the field of special functions, especially confluent hypergeometric functions Teri Perl (B.A. 1947), mathematics educator, co-founder
List of Brooklyn College alumni
List_of_Brooklyn_College_alumni
(1960), Confluent hypergeometric functions, Cambridge, UK: Cambridge University Press, Slater, Lucy Joan (1966), Generalized hypergeometric functions, Cambridge
Timeline of women in mathematics
Timeline_of_women_in_mathematics
{J_{s}(z{\sqrt {1-x^{2}}})}{{\sqrt {1-x^{2}}}^{s}}}\,dx,} the confluent hypergeometric function M ( a , s , z ) = Γ ( s ) ∑ k = 0 ∞ ( − 1 t ) k L k ( − a
Neumann_polynomial
Physical interaction of charged particles
applying parabolic coordinates leading to solutions in terms of confluent hypergeometric functions. The broadly applied workaround for the divergence of the
Coulomb_scattering
Pattern defining an infinite sequence of numbers
solved by M n = M ( n , b ; z ) {\displaystyle M_{n}=M(n,b;z)} the confluent hypergeometric series. Sequences which are the solutions of linear difference
Recurrence_relation
Physical interaction in post-classical physics
{r_{12}}{r_{B}}}\right)}} where M {\displaystyle M} is a confluent hypergeometric function or Kummer function. In obtaining the interaction energy we have used
Static forces and virtual-particle exchange
Static_forces_and_virtual-particle_exchange
Array in complex analysis
applied to a certain confluent hypergeometric series to derive the following C-fraction expansion for the exponential function, valid throughout the
Padé_table
Stochastic process
{\displaystyle a_{j}} are the zeros of the Airy function and U {\displaystyle U} is the confluent hypergeometric function. Janson and Louchard (2007) show that
Brownian_excursion
British schoolteacher, mathematician and astrophysicist (1868–1937)
transcendental functions), the Lommel-Weber function and the confluent hypergeometric functions. In a collation of notable mathematical table makers, Archibald
John_Robinson_Airey
z ) {\displaystyle _{1}F_{1}(a,b;z)} is the Kummer confluent hypergeometric function. This function has usually very good convergence properties and is
Generalized integer gamma distribution
Generalized_integer_gamma_distribution
American mathematician (born 1945)
characteristic p. In particular, he related these sums to certain classical confluent hypergeometric differential equations. This relationship generalized the study
Steven_Sperber
Probability distribution
subsets. The characteristic function of the Dirichlet distribution is a confluent form of the Lauricella hypergeometric series. It is given by Phillips
Dirichlet_distribution
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
Boy/Male
Tamil
Manifested, Confident
Girl/Female
Hindu
Confident
Boy/Male
African, Arabic
Confident; Generous
Boy/Male
Hindu, Indian, Kannada, Tamil
Brave; Confident
Boy/Male
Arabic
Confident; Strong
Boy/Male
Tamil
Manifested, Confident
Boy/Male
Indian
Confident; Great
Boy/Male
Hindu
Manifested, Confident
Boy/Male
Arabic
Confident
Girl/Female
Hindu, Indian, Sindhi
Self-confident
Boy/Male
Tamil
Manifested, Confident
Boy/Male
Indian, Kannada, Tamil
Confident
Boy/Male
Hindu
Manifested, Confident
Girl/Female
Tamil
Prathitha | பà¯à®°à®¤à¯€à®¤à®¾
Confident
Prathitha | பà¯à®°à®¤à¯€à®¤à®¾
Girl/Female
Muslim
Steady, Confident
Boy/Male
Tamil
Self confident
Boy/Male
Hindu, Indian
Confident
Girl/Female
Arabic, French, Indian, Kannada, Muslim
Steady; Confident
Boy/Male
Arabic
Confident; Strong
Boy/Male
Hindu
Manifested, Confident
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
Girl/Female
Bengali, Hindu, Indian, Kannada, Tamil
Truth of Life; Jewel
Girl/Female
Tamil
Sulakshana | ஸà¯à®²à®•à¯à®·à®£à®¾
Well brought up, Fortunate
Girl/Female
Tamil
Samskruti | ஸஂஸà¯à®•à®°à®¤à®¿Â
Being traditional
Girl/Female
Muslim
Most perfect, Complete
Girl/Female
Tamil
Young girl
Boy/Male
Tamil
Exerting
Girl/Female
German, Hungarian
Renowned Battle; Famous Battle
Surname or Lastname
English
English : patronymic from the nickname Cousin.
Male
English
Variant spelling of English unisex Mahalah, MAHALA means "disease."Â
Female
African
faith.
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
CONFLUENT HYPERGEOMETRIC-FUNCTION
v. i.
To be assured; to feel confident.
n.
Any running together of separate streams or currents; the act of meeting and crowding in a place; hence, a crowd; a concourse; an assemblage.
a.
Blended into one; growing together, so as to obliterate all distinction.
a.
Unduly confident; arrogant; presumptuous; conceited.
a.
Bold; confident; free from depression; undismayed.
a.
Characterized by having the pustules, etc., run together or unite, so as to cover the surface; as, confluent smallpox.
a.
Running together or uniting, as pimples or pustules.
a.
Flowing together; meeting in their course; running one into another.
n.
The quality of being confident.
n.
One who confesses his sins and faults.
prep.
Violent confluence.
a.
Not assured; not bold or confident.
n.
See Confidant.
n.
The act of flowing together; the meeting or junction of two or more streams; the place of meeting.
a.
Possessing congruity; suitable; agreeing; corresponding.
n.
The place of meeting of steams, currents, etc.
a.
Made confident by drink.
n.
A small steam which flows into a large one.
a.
Confident to excess.
a.
Confident of one's own strength or powers; relying on one's judgment or ability; self-reliant.