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Special mathematical function
In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only
Polylogarithm
mathematics, the incomplete polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral
Incomplete_polylogarithm
the incomplete Fermi-Dirac integral for non-positive indices j {\displaystyle j} . This is an alternate definition of the incomplete polylogarithm, since:
Incomplete Fermi–Dirac integral
Incomplete_Fermi–Dirac_integral
Polylogarithm and related functions: Incomplete polylogarithm Clausen function Complete Fermi–Dirac integral, an alternate form of the polylogarithm.
List of mathematical functions
List_of_mathematical_functions
Formula for the thermal radiation emitted by a perfect black body
yields an incomplete polylogarithm function, which can make its use very cumbersome. The standard numerical treatment expands the incomplete integral in
Sakuma–Hattori_equation
Mathematical integral
{\displaystyle \eta } is the Dirichlet eta function. Incomplete Fermi–Dirac integral Gamma function Polylogarithm Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif
Complete_Fermi–Dirac_integral
Special mathematical function
special function that generalizes the Hurwitz zeta function and the polylogarithm. It is named after Czech mathematician Mathias Lerch, who published
Lerch_transcendent
Analytic function in mathematics
related functions see the articles zeta function and L-function. The polylogarithm is given by Li s ( z ) = ∑ k = 1 ∞ z k k s {\displaystyle \operatorname
Riemann_zeta_function
where Li s ( z ) {\displaystyle \operatorname {Li} _{s}(z)} is the Polylogarithm. ∫ 0 ∞ sin m x e 2 π x − 1 d x = 1 4 coth m 2 − 1 2 m {\displaystyle
List of integrals of exponential functions
List_of_integrals_of_exponential_functions
Operation on formal power series
the special case of the integral formula for the Nielsen generalized polylogarithm function defined in) ∑ n ≥ 0 f n ( n + 1 ) s z n = ( − 1 ) s − 1 ( s
Generating function transformation
Generating_function_transformation
Mathematical function
called the Debye model. The Debye functions are closely related to the polylogarithm. They have the series expansion D n ( x ) = 1 − n 2 ( n + 1 ) x + n
Debye_function
History of maths
phenomena in as diverse areas as: Hodge theory, algebraic K-theory, polylogarithms, regulator maps, automorphic forms, L-functions, ℓ-adic representations
Timeline of category theory and related mathematics
Timeline_of_category_theory_and_related_mathematics
Sum of the first n whole number reciprocals; 1/1 + 1/2 + 1/3 + ... + 1/n
where Li m ( z ) {\displaystyle \operatorname {Li} _{m}(z)} is the polylogarithm, and |z| < 1. The generating function given above for m = 1 is a special
Harmonic_number
Table of integrals compiled by I. S. Gradshteyn and I. M. Ryzhik
(2012-07-28) [2012-02-01]. "The integrals in Gradshteyn and Ryzhik. Part 24: Polylogarithm functions" (PDF). Scientia. Series A: Mathematical Sciences. 23 (published
Gradshteyn_and_Ryzhik
Family of power series in mathematics
\mathbb {N} _{0}} and p ∈ N {\displaystyle p\in \mathbb {N} } are the Polylogarithm. For each integer n≥2, the roots of the polynomial xn−x+t can be expressed
Generalized hypergeometric function
Generalized_hypergeometric_function
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
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Incomplete
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Complete
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Complete
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Grand; Incomplete
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Complete
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Complete
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Incomplete
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Complete
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Complete
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Complete
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Complete
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Indian
Complete
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Muslim
Complete
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Muslim
Complete
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Complete
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Complete
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Complete
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Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
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Hindu
Complete
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
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Happiness
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Arabic, Bengali, German, Hebrew, Hindu, Indian, Marathi, Muslim, Telugu, Turkish
Expert; Industrious; Skilled
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Most Generous; Most Bountiful
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Muslim
Unique
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Bright Light
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American, Australian, Biblical, British, Chinese, Christian, Danish, English, German, Greek, Latin
From the Forest or Woods; Three; The Third; Wood Dweller
Boy/Male
Hindu, Indian, Marathi, Oriya
One who has been Invited; Wanted
Girl/Female
Biblical
Sweet scent.
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Devout believer, Submitting oneself to God
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Joyful World; Happy Peace; Great; Famous; Caring
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
n.
An incomplete or partial dislocation.
adv.
In an incomplete manner.
a.
Wanting any of the usual floral organs; -- said of a flower.
n.
An incomplete or partial shadow.
a.
Incomplete.
adv.
In a sketchy or incomplete manner.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
a.
Not complex; uncompounded; simple.
a.
Full; complete.
n.
The state of being incomplete; imperfectness; defectiveness.
n.
Complete termination.
n.
Incomplete correspondence.
a.
Filled up; with no part or element lacking; free from deficiency; entire; perfect; consummate.
a.
Not consummated; not finished; incomplete.
a.
Having all the parts or organs which belong to it or to the typical form; having calyx, corolla, stamens, and pistil.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Making complete.
n.
Incomplete paralysis, affecting motion but not sensation.
n. pl.
Those insects which have an incomplete metamorphosis.
a.
Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective.