Lemniscate-like constants and infinite series-Reference-Cited by-同舟云学术

Lemniscate-like constants and infinite series

Published:2021-08-01 Issue:4 Volume:71 Page:845-858
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Campbell John M.¹,Chu Wenchang²

Affiliation:

1. Department of Mathematics and Statistics , York University , Toronto, Ontario , Canada

2. Department of Mathematics and Physics , University of Salento (P. O. Box 193) , Lecce Italy

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2021-0025/pdf

Reference29 articles.

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3. Berndt, B. C.—Bhargava, S.: Ramanujan's inversion formulas for the lemniscate and allied functions, J. Math. Anal. Appl. 160 (1991), 504–524.

4. Boyadzhiev, K. N.: Series with central binomial coefficients, Catalan numbers, and harmonic numbers, J. Integer Seq. 15 (2012), Art. 12.1.7.

5. Campbell, J. M.: Ramanujan-like series for1π$\frac{1}{\pi}$involving harmonic numbers, Ramanujan J. 46 (2018), 373–387.

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