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On Meromorphic Harmonic Functions Associated with the Polylogarithm Function
MathematicsThis paper examines the relationship between the classical polylogarithm function and meromorphic harmonic univalent mappings. Using a convolution operator derived from the polylogarithm function, we define a class of harmonic meromorphic functions and ...
Huda Ali Aldweby
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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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The Bloch-Wigner-Ramakrishnan polylogarithm function
Mathematische Annalen, 1990 The dilogarithm function Li\\sb 2(z)=\\sum\\sp∞\\sbn=1z\\sp n/n\\sp 2 (\\vert z\\vert lt;1) has many beautiful properties and plays a role in connection with problems in many parts of mathematics, most recently K-theory. This function cannot be extended in a one-valued way to the entire complex plane, but the modified function D(z)=\\cal I(Li\\sb 2(z)+\
Don Zagier
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Discrete Polylogarithm Functions [PDF]
Tatra Mountains Mathematical Publications, 2023 Abstract We investigate a discrete analogue of the polylogarithm function. Difference and summation relations are obtained, as well as its connection to the discrete hypergeometric series.
Cuchta, Tom, Freeman, Dallas
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Various Series Related to the Polylogarithmic Function [PDF]
Axioms, 2022 We derive some series related to the polylogarithmic function, and we also give a new proof to the existing series. Our approach is based on using the summation and integral representation methods. We obtain various interesting series as a consequence.
Vuk Stojiljkovic +5 more
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On functional equations for Nielsen polylogarithms [PDF]
Communications in Number Theory and Physics, 2021 36 pages, 3 ...
Charlton, Steven +2 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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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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Harmonic series with polylogarithmic functions [PDF]
Vojnotehnicki glasnik, 2022 Introduction/purpose: Some sums of the polylogarithmic function associated with harmonic numbers are established. Methods: The approach is based on using the summation methods. Results: This paper generalizes the results of the zeta function series associated with the harmonic numbers.
Vuk Stojiljković +2 more
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