A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums

Takumi Maesaka

A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums

Number Theory 2026-08-11 v1 Classical Analysis and ODEs

Authors: Takumi Maesaka

Abstract

We prove a double-sum analogue of Whipple's ${}_3F_2$ summation formula. As an application, we establish a restricted sum formula for multiple binomial sums, which arise as special cases of Igarashi's parametrized multiple zeta series.

Keywords

Whipple summation formula double-sum analogue restricted sum formula multiple binomial sums multiple zeta series

Cite

@article{arxiv.2608.10984,
  title  = {A double-sum analogue of Whipple's summation formula and a restricted sum formula for multiple binomial sums},
  author = {Takumi Maesaka},
  journal= {arXiv preprint arXiv:2608.10984},
  year   = {2026}
}

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11 pages