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Lemniscate-like constants and infinite series

  • John M. Campbell EMAIL logo and Wenchang Chu
Published/Copyright: August 1, 2021
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Abstract

We introduce lemniscate-like constants by “twisting” the standard series expansions of the classical lemniscate constants via harmonic-type factors in the summand. Closed-form evaluations for these constants are established, and are then utilized to construct alternate proofs of summation formulae obtained recently via coefficient-extraction techniques applied to Kummer’s classical hypergeometric identity.

  1. (Communicated by Tomasz Natkaniec)

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Received: 2020-04-19
Accepted: 2020-12-18
Published Online: 2021-08-01
Published in Print: 2021-08-26

© 2021 Mathematical Institute Slovak Academy of Sciences

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