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A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants

Integers, 2012
.Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous experimentally discovered
Kunle Adegoke
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Meromorphic functions connected with polylogarithms

Functional Analysis and Its Applications, 1991
The polylogarithm \[ Li_ m(z)= \sum_{n=1}^ \infty z^ n/n^ m \] cannot be extended to a continuous one-valued function on the whole complex plane. There are a number of suggested remedies: for example, \textit{D. Zagier} [``Special values and functional equations of polylogarithms'', in L.
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Polylogarithms and Riemann’s ζ function

Physical Review E, 1997
Riemann’s z function perhaps first appeared in statistical mechanics in 1900 in Planck’s theory of the blackbody radiation and then in 1912 in Debye’s theory of the specific heats of solids @1#. Subsequently, this function has played an important role in the statistical theory of the ideal Bose gas, especially for the understanding of Bose-Einstein ...
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Blackbody radiation functions and polylogarithms

Journal of Quantitative Spectroscopy and Radiative Transfer, 2012
A new method based on the polylogarithm function is used to derive an exact expression for the fractional emissive power of a blackbody in any arbitrary spectral band. Compared to all previously used methods the polylogarithm based method is unsurpassed in its simplicity.
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Polylogarithmic zeta functions and their p-adic analogues

International Journal of Number Theory, 2017
We consider a broad family of zeta functions which includes the classical zeta functions of Riemann and Hurwitz, the beta and eta functions of Dirichlet, and the Lerch transcendent, as well as the Arakawa–Kaneko zeta functions and the recently introduced alternating Arakawa–Kaneko zeta functions.
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Integrals of inverse trigonometric and polylogarithmic functions

The Ramanujan Journal, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON POLYLOGARITHMS, HURWITZ ZETA FUNCTIONS, AND THE KUBERT IDENTITIES

1983
This very interesting and rich paper deals with classical analytic functions put in a new light, using modern techniques. It deals with the Hurwitz zeta-function \[ \zeta_{1- s}(x)=\sum^{\infty}_{n=0}(n+x)^{s-1} \] and the Fourier series (vid polylog) \(\ell_ s(x)=\sum e^{2\pi inx}n^{-s}\). Both functions are special cases of Lerch zeta-function. There
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Integrals of polylogarithmic functions with alternating argument

Asian-European Journal of Mathematics, 2019
The connection between polylogarithmic functions and Euler sums is well-known. In this paper, we explore the representation and many connections between integrals of products of polylogarithmic functions with alternating signs in the argument and Euler sums.
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Explicit evaluation of some integrals involving polylogarithm functions

Integral Transforms and Special Functions, 2022
Rusen Li
exaly  

The Polylogarithm Function.

Arch. Formal Proofs, 2023
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