Applications of Symmetric Identities for Apostol–Bernoulli and Apostol–Euler Functions

In this paper, we perform a further investigation on the Apostol–Bernoulli and Apostol–Euler functions introduced by Luo. By using the Fourier expansions of the Apostol–Bernoulli and Apostol–Euler polynomials, we establish some symmetric identities for the Apostol–Bernoulli and Apostol–Euler functio...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 15; no. 7; p. 1384
Main Author He, Yuan
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2023
Subjects
Apostol–Bernoulli functions
Apostol–Euler functions
Bernoulli functions
combinatorial identity
Identities
Mathematical analysis
Polynomials
quasi-periodic Euler functions
Symmetry
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Summary:In this paper, we perform a further investigation on the Apostol–Bernoulli and Apostol–Euler functions introduced by Luo. By using the Fourier expansions of the Apostol–Bernoulli and Apostol–Euler polynomials, we establish some symmetric identities for the Apostol–Bernoulli and Apostol–Euler functions. As applications, some known results, for example, Raabe’s multiplication formula and Hermite’s identity, are deduced as special cases.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym15071384