Results 31 to 40 of about 562 (207)
Proceedings of the Glasgow Mathematical Association, 1964 The nth order polylogarithm Lin(z) is defined for |z| ≦ 1 by([4, p. 169], cf. [2, §1. 11 (14) and § 1. 11. 1]). The definition can be extended to all values of zin the z-plane cut along the real axis from 1 to ∝ by the formula[2, §1. 11(3)]. Then Lin(z) is regular in the cut plane, and there is a differential recurrence relation [4, p.
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Optimal Stein‐type goodness‐of‐fit tests for count data
Biometrical Journal, Volume 65, Issue 2, February 2023., 2023 Abstract Common count distributions, such as the Poisson (binomial) distribution for unbounded (bounded) counts considered here, can be characterized by appropriate Stein identities. These identities, in turn, might be utilized to define a corresponding goodness‐of‐fit (GoF) test, the test statistic of which involves the computation of weighted means ...
Christian H. Weiß +2 more
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Simplifying polylogarithms with machine learning
International Journal of Data Science in the Mathematical Sciences, 2023 Polylogarithmic functions, such as the logarithm or dilogarithm, satisfy a number of algebraic identities. For the logarithm, all the identities follow from the product rule. For the dilogarithm and higher-weight classical polylogarithms, the identities can involve five functions or more.
Aurélien Dersy +2 more
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On Degenerate Poly‐Daehee Polynomials Arising from Lambda‐Umbral Calculus
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 In this article, we derived various identities between the degenerate poly‐Daehee polynomials and some special polynomials by using λ‐umbral calculus by finding the coefficients when expressing degenerate poly‐Daehee polynomials as a linear combination of degenerate Bernoulli polynomials, degenerate Euler polynomials, degenerate Bernoulli polynomials ...
Sang Jo Yun, Jin-Woo Park, M. M. Bhatti
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Nagoya Mathematical Journal, 1989 Some functions related to the complex dilogarithmic function(in the notation of Lewin [9]) are known to occur in connection with algebraic K-theory and characteristic classes (see e.g. Bloch [1], Gelfand-MacPherson [7], Dupont [5], and the references given there).
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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, 2017 The article considers a mixed problem with homogeneous boundary conditions for onedimensional homogeneous wave equation. Such a problem can arise, for example, when studying oscillations of current and voltage in the conductor through which electric ...
P. G. Lasy, I. N. Meleshko
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The Hodge Realization of the Polylogarithm and the Shintani Generating Class for Totally Real Fields [PDF]
, 2023 In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne-Beilinson cohomology of a certain algebraic torus associated to a totally real field.
Ohshita, Tatsuya +5 more
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Representation of some special functions on transcendence basis
Tạp chí Khoa học Đại học Huế: Khoa học Tự nhiên, 2020 The special functions such as multiple harmonic sums, polyzetas or multiple polylogarithm functions are compatible with quasi-shuffle algebras. By using transcendence bases of the quasi-shuffle algebras studied in the paper [4], we will express non ...
Bui Van Chien
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Clean Single-Valued Polylogarithms [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 We define a variant of real-analytic polylogarithms that are single-valued and that satisfy ''clean'' functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results.
Charlton, S. ; https://orcid.org/0000-0002-2815-1885 +2 more
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