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On the fractional sums of some special functions

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Publication:667592
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DOI10.1007/s00025-019-0964-4zbMath1468.11181OpenAlexW2914674019WikidataQ128445506 ScholiaQ128445506MaRDI QIDQ667592

Banu Ünalmış Uzun

Publication date: 28 February 2019

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-019-0964-4

zbMATH Keywords

polylogarithmRiemann \(\zeta\) functionfractional sumHurwitz \(\zeta\) functionLerch transcendent


Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Gamma, beta and polygamma functions (33B15) Hurwitz and Lerch zeta functions (11M35)



Uses Software

  • Equator


Cites Work

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  • An Euler-type formula for \(\xi (2k+1)\)
  • Double integrals and infinite products for some classical constants via analytic continuations of Lerch's transcendent
  • Some formulas related to Hurwitz-Lerch zeta functions
  • Derivatives of the Hurwitz zeta function for rational arguments
  • How to add a non-integer number of terms, and how to produce unusual infinite summations
  • Fractional sums and Euler-like identities
  • How to Add a Noninteger Number of Terms: From Axioms to New Identities
  • An Euler-type formula forβ(2n) and closed-form expressions for a class of zeta series
  • Closed-Form Summation of Some Trigonometric Series
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