Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-25T10:03:13.115Z Has data issue: false hasContentIssue false

An extension of the curious binomial identity of Simons

Published online by Cambridge University Press:  23 August 2024

Necdet Batir
Affiliation:
Department of Mathematics, Nevşehir Haci Bektaş Veli University, Nevşehir, 50300 Turkey e-mails: [email protected], [email protected], [email protected]
Sevda Atpinar
Affiliation:
Department of Mathematics, Nevşehir Haci Bektaş Veli University, Nevşehir, 50300 Turkey e-mails: [email protected], [email protected], [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In 2001 Simons [1] discovered a curious binomial identity which can be written as(1)

Type
Articles
Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

References

Simons, S., A curious identity, Math. Gaz. 85 (July 2001) pp. 296298.CrossRefGoogle Scholar
Chapman, R., A curious identity revisited, Math. Gaz. 87 (March 2003) pp. 139141.CrossRefGoogle Scholar
Prodinger, H., A curious identity proved by Cauchy’s integral formula, Math. Gaz. 89 (July 2005) pp. 266267.CrossRefGoogle Scholar
Wang, X. and Sun, Y., A new proof of a curious identity, Math. Gaz. 91 (March 2007) pp. 105106.CrossRefGoogle Scholar
Munarini, E., Generalization of a binomial identity of Simons, Integers: Electron. J. Combin. Number Theory, 5 (2005) A15.Google Scholar
Wei, C., Wei, Y. and Li, C., Some summation and transformation formulas from inversion techniques, Integers, 22 (2022) A95.Google Scholar
Shattuck, M., Combinatorial proofs of some Simons-type binomial coefficient identities, Integers: Electron. J. Combin. Number Theory, 7 (2007) A27.Google Scholar
Hirschhorn, M., Comments on a curious identity, Math. Gaz. 87 (November 2003) pp. 528530.CrossRefGoogle Scholar
Xu, A. and Cen, Y., Combinatorial identities from contour integrals, Ramanujan J., 40 (2016) pp. 103114.CrossRefGoogle Scholar
Batir, N. and Sofo, A., Finite sums involving reciprocals of the binomial and central binomial coefficients and harmonic numbers, Symmetry, 13(11) (2021)CrossRefGoogle Scholar
Sved, M., Counting and recounting, Math. Intelligencer, 4 (1983) pp. 2126.CrossRefGoogle Scholar
Batir, N., Küçük, H. and Sorgun, S., Convolution identities involving the central binomial coefficients and Catalan numbers, Transactions on Combinatorics, 10 (2021) pp. 225238.Google Scholar
Sved, M., Counting and recounting: the aftermath, Math. Intelligencer, 6 (1984) pp. 4446.CrossRefGoogle Scholar