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Evaluation of the real parts of polylogarithm expressions containing complex arguments via certain logarithmic integrals [PDF]
Notes on Number Theory and Discrete MathematicsWe consider a polylogarithm expression containing complex arguments, namely 𝓟±(n)=ℜ(Liₙ((1±i)/2)). The central notion of the present paper is to evaluate the real parts of 𝓟±(n) for first four orders, specifically n = 1,2,3, and 4, by constructing ...
Narendra Bhandari
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The Cotangent Function as an Avatar of the Polylogarithm Function of Order 0 and Ramanujan’s Formula
AxiomsIn this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Fraction Expansion ...
Ruiyang Li +2 more
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Representations of degenerate poly-Bernoulli polynomials
Journal of Inequalities and Applications, 2021 As is well known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate versions of such functions and polynomials, degenerate polylogarithm functions were introduced and degenerate poly-Bernoulli polynomials
Taekyun Kim +3 more
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A New Family of Degenerate Poly-Genocchi Polynomials with Its Certain Properties
Journal of Function Spaces, 2021 In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called degenerate poly-Genocchi polynomials and numbers, by using the degenerate polylogarithm function, and we derive several properties of these ...
Waseem A. Khan +3 more
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On the new type of degenerate poly-Genocchi numbers and polynomials
Advances in Difference Equations, 2020 Kim and Kim (J. Math. Anal. Appl. 487:124017, 2020) introduced the degenerate logarithm function, which is the inverse of the degenerate exponential function, and defined the degenerate polylogarithm function.
Dae Sik Lee, Hye Kyung Kim
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Degenerate poly-Bernoulli polynomials arising from degenerate polylogarithm
Advances in Difference Equations, 2020 Recently, degenerate polylogarithm functions were introduced by Kim and Kim. In this paper, we introduce degenerate poly-Bernoulli polynomials by means of the degenerate polylogarithm functions and investigate some their properties.
Taekyun Kim +4 more
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Notes on Meromorphic Functions with Positive Coefficients Involving Polylogarithm Function
Известия Иркутского государственного университета: Серия "Математика", 2020 In this paper, we introduce and study a new subclass of meromorphic functions with positive coefficients involving the polylogarithm function and obtain coefficient estimates, growth and distortion theorem, radius of convexity, integral transforms ...
G. Swapna +2 more
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Wien peaks and the Lambert W function [PDF]
Revista Brasileira de Ensino de Física, 2011 Exact expressions for the wavelengths where maxima occur in the spectral distribution curves of blackbody radiation for a number of diferent dispersion rules are given in terms of the Lambert W function.
Seán M. Stewart
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On criteria for algebraic independence of collections of functions satisfying algebraic difference relations [PDF]
Opuscula Mathematica, 2017 This paper gives conditions for algebraic independence of a collection of functions satisfying a certain kind of algebraic difference relations. As applications, we show algebraic independence of two collections of special functions: (1) Vignéras ...
Hiroshi Ogawara
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Известия высших учебных заведений и энергетических объединенний СНГ: Энергетика, 2019 The paper deals with a mixed problem for the telegraph equation well-known in electrical engineering and electronics, provided that the line is free from distortion.
P. G. Lasy, I. N. Meleshko
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