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Evaluations of some Euler-Apéry-type series

Author

Listed:
  • Yujie Wang

    (Anhui Normal University)

  • Ying Li

    (Anhui Normal University)

  • Ce Xu

    (Anhui Normal University)

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.

Suggested Citation

  • Yujie Wang & Ying Li & Ce Xu, 2022. "Evaluations of some Euler-Apéry-type series," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(4), pages 849-864, December.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:4:d:10.1007_s13226-021-00191-9
    DOI: 10.1007/s13226-021-00191-9
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