Infinite Series Associated with the Ratio and Product of Central Binomial Coefficients
Department of Mathematics
University of Delhi
We establish several interesting series associated with the ratio and
the product of central binomial coefficients, namely
. Series involving the product of central binomial coefficients
can be found in the papers of Campbell, D'Aurizio, and Sondow. In this
paper, through the application of integration methods, we
address broad generalizations of both classes. The techniques involved
in constructing the integrals for the corresponding series are
based on the use of the ordinary generating functions of central binomial
coefficients and Wallis' well-known integral formulas.
Full version: pdf,
(Concerned with sequence
Received April 15 2022;
revised versions received April 27 2022; June 22 2022; June 26 2022;
June 27 2022.
Published in Journal of Integer Sequences,
June 29 2022.
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