Evaluations of some Euler-Apéry-type series

Yujie Wang (), Ying Li () and Ce Xu ()
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Yujie Wang: Anhui Normal University
Ying Li: Anhui Normal University
Ce Xu: Anhui Normal University

Indian Journal of Pure and Applied Mathematics, 2022, vol. 53, issue 4, 849-864

Abstract: Abstract In this paper, we use the methods of contour integration and generating function involving Fuss-Catalan numbers to study some Euler-Apéry-type series. In particular, we obtain some explicit formulas for some Euler-Apéry-type series. Based on these formulas, we further show that some series are reducible to logarithms (such as: $$\log (2),\log (3),\log (5)$$ log ( 2 ) , log ( 3 ) , log ( 5 ) etc.), zeta values and multiple polylogarithms. Moreover, we establish a recurrence relation for general Euler-Apéry-type series involving multiple harmonic star sum. Furthermore, some interesting new consequences and illustrative examples are considered.

Keywords: Euler-Apéry-type series; Contour integration; Fuss-Catalan numbers; Generating function; 65B10; 11B65; 11M32 (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13226-021-00191-9

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