Journal of Integer Sequences, Vol. 25 (2022), Article 22.1.8

Interesting Ramanujan-Like Series Associated with Powers of Central Binomial Coefficients

Hongwei Chen
Department of Mathematics
Christopher Newport University
Newport News, VA 23606


We find various Ramanujan-like series that involve the central binomial coefficients. In contrast with the traditional hypergeometric function approach, our method uses Fourier-Legendre series expansions via specialization, inner product, and Parseval's identity. Several classical identities are recovered as particular cases.

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(Concerned with sequences A000045 A000984 A001008 A005408.)

Received October 8 2021; revised version received January 5 2022. Published in Journal of Integer Sequences, January 28 2022.

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