Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-25T17:20:41.192Z Has data issue: false hasContentIssue false
  • English
  • Français

An extension of the curious binomial identity of Simons

Published online by Cambridge University Press:  23 August 2024

Necdet Batir  and
Sevda Atpinar
Necdet Batir
Affiliation:
Department of Mathematics, Nevşehir Haci Bektaş Veli University, Nevşehir, 50300 Turkey e-mails: nbatir@hotmail.com, nbatir@nevsehir.edu.tr, sevdaatpinar@nevsehir.edu.tr
Sevda Atpinar
Affiliation:
Department of Mathematics, Nevşehir Haci Bektaş Veli University, Nevşehir, 50300 Turkey e-mails: nbatir@hotmail.com, nbatir@nevsehir.edu.tr, sevdaatpinar@nevsehir.edu.tr
Get access Rights & Permissions [Opens in a new window]

Extract

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

Type
Articles
Information
The Mathematical Gazette , Volume 108 , Issue 572 , July 2024 , pp. 270 - 274
Check for updates
Copyright
© The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Simons, S., A curious identity, Math. Gaz. 85 (July 2001) pp. 296–298.10.2307/3622028CrossRefGoogle Scholar
Chapman, R., A curious identity revisited, Math. Gaz. 87 (March 2003) pp. 139–141.10.1017/S0025557200172328CrossRefGoogle Scholar
Prodinger, H., A curious identity proved by Cauchy’s integral formula, Math. Gaz. 89 (July 2005) pp. 266–267.CrossRefGoogle Scholar
Wang, X. and Sun, Y., A new proof of a curious identity, Math. Gaz. 91 (March 2007) pp. 105–106.10.1017/S0025557200181094CrossRefGoogle 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. 528–530.10.1017/S0025557200173838CrossRefGoogle Scholar
Xu, A. and Cen, Y., Combinatorial identities from contour integrals, Ramanujan J., 40 (2016) pp. 103–114.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. 21–26.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. 225–238.Google Scholar
Sved, M., Counting and recounting: the aftermath, Math. Intelligencer, 6 (1984) pp. 44–46.10.1007/BF03026737CrossRefGoogle Scholar