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Volume 11
Issue 4
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Article

On a Family of Infinite Series with Reciprocal Catalan Numbers

by
Kunle Adegoke
1,
Robert Frontczak
2,*,† and
Taras Goy
3
1
Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria
2
Landesbank Baden-Württemberg, 70173 Stuttgart, Germany
3
Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 76018 Ivano-Frankivsk, Ukraine
*
Author to whom correspondence should be addressed.
†
Statements and conclusions made in this article by R. Frontczak are entirely those of the author. They do not necessarily reflect the views of LBBW.
Axioms 2022, 11(4), 165; https://doi.org/10.3390/axioms11040165
Submission received: 13 January 2022 / Revised: 21 March 2022 / Accepted: 24 March 2022 / Published: 7 April 2022
(This article belongs to the Section Mathematical Analysis)
Versions Notes

Abstract

We study a certain family of infinite series with reciprocal Catalan numbers. We first evaluate two special candidates of the family in closed form, where we also present some Catalan–Fibonacci relations. Then, we focus on the general properties of the family and prove explicit formulas, including two types of integral representations.
Keywords: Catalan numbers; infinite series; Fibonacci numbers; Lucas numbers; Stirling numbers; Mellin transform Catalan numbers; infinite series; Fibonacci numbers; Lucas numbers; Stirling numbers; Mellin transform

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MDPI and ACS Style

Adegoke, K.; Frontczak, R.; Goy, T. On a Family of Infinite Series with Reciprocal Catalan Numbers. Axioms 2022, 11, 165. https://doi.org/10.3390/axioms11040165

AMA Style

Adegoke K, Frontczak R, Goy T. On a Family of Infinite Series with Reciprocal Catalan Numbers. Axioms. 2022; 11(4):165. https://doi.org/10.3390/axioms11040165

Chicago/Turabian Style

Adegoke, Kunle, Robert Frontczak, and Taras Goy. 2022. "On a Family of Infinite Series with Reciprocal Catalan Numbers" Axioms 11, no. 4: 165. https://doi.org/10.3390/axioms11040165

APA Style

Adegoke, K., Frontczak, R., & Goy, T. (2022). On a Family of Infinite Series with Reciprocal Catalan Numbers. Axioms, 11(4), 165. https://doi.org/10.3390/axioms11040165

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