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mathematics, the incomplete polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral
Incomplete_polylogarithm
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
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
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
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
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
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INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
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Name of a Raga
Surname or Lastname
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English : possibly an altered spelling of Chapman.Perhaps also an Americanized spelling of German Schattmann, a North German form of Schatzmann (see Schatzman).
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Joyful unending, Calmness
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A worshipper of Lord Shiva
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Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Sindhi, Telugu, Traditional
One who has Conquered the Sky
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Tamed; Conforming
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Graceful, Good looking
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Wealthy Spear-man; Fortunate and Powerful; God Spear; Lucky Spearman; Rich Spear
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Love with God
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
INCOMPLETE POLYLOGARITHM
n.
An incomplete or partial dislocation.
a.
Incomplete.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
Incomplete paralysis, affecting motion but not sensation.
n. pl.
Those insects which have an incomplete metamorphosis.
a.
Making complete.
a.
Having all the parts or organs which belong to it or to the typical form; having calyx, corolla, stamens, and pistil.
adv.
In an incomplete manner.
n.
The state of being incomplete; imperfectness; defectiveness.
a.
Not consummated; not finished; incomplete.
a.
Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective.
a.
Not complex; uncompounded; simple.
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.
Full; complete.
a.
Filled up; with no part or element lacking; free from deficiency; entire; perfect; consummate.
adv.
In a sketchy or incomplete manner.
n.
Incomplete correspondence.
a.
Wanting any of the usual floral organs; -- said of a flower.
n.
Complete termination.
n.
An incomplete or partial shadow.