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PreprintCC BY 4.0arXiv

Extensions of several famous combinatorial identities via hypergeometric functions

  • Arjun Kumar Rathie
  • Feng Qi
  • Dongkyu Lim
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Abstract

The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.

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Cite

BibTeXRIS
BibTeX
@misc{rathie2026extensions,
  title = {{Extensions of several famous combinatorial identities via hypergeometric functions}},
  author = {Arjun Kumar Rathie and Feng Qi and Dongkyu Lim},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.05192},
  eprint = {2608.05192},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.05192},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Extensions of several famous combinatorial identities via hypergeometric functions
AU  - Arjun Kumar Rathie
AU  - Feng Qi
AU  - Dongkyu Lim
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.05192
UR  - https://arxiv.org/abs/2608.05192
AB  - The objective of this paper is to develop an extension of Kummer's second theorem and to establish generalized forms of four classical combinatorial identities---Knuth's old sum (also known as Reed--Dawson's combinatorial identity), Riordan's combinatorial identity, Gould's combinatorial identity, and Touchard's combinatorial identity---using a hypergeometric-series approach. Several new identities also arise as special cases of our main results.
ER  -