On a Family of Infinite Series with Reciprocal Catalan Numbers

被引：1

作者：

Adegoke, Kunle ^{[1
]}

Frontczak, Robert ^{[2
]}

Goy, Taras ^{[3
]}

机构：

[1] Obafemi Awolowo Univ, Dept Phys & Engn Phys, Ife 220005, Nigeria

[2] Landesbank Baden Wurttemberg, D-70173 Stuttgart, Germany

[3] Vasyl Stefanyk Precarpathian Natl Univ, Fac Math & Comp Sci, UA-76018 Ivano Frankivsk, Ukraine

来源：

AXIOMS | 2022年 / 11卷 / 04期

关键词：

Catalan numbers; infinite series; Fibonacci numbers; Lucas numbers; Stirling numbers; Mellin transform; GENERATING-FUNCTIONS; POLYNOMIALS; POWERS; SUMS;

D O I：

10.3390/axioms11040165

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：14

共 31 条

[1] Abel U, 2016, AM MATH MON, V123, P405
[2] Adegoke K., 2022, PALESTINE MATH J, V11, P66
[3] Adegoke K., 2021, ARXIV211200622
[4] A series involving Catalan numbers: Proofs and demonstrations
Amdeberhan, T.
Guan, X.
Jiu, L.
Moll, V. H.
Vignat, C.
[J]. ELEMENTE DER MATHEMATIK, 2016, 71 (03) : 109 - 121
[5] Barry P., 2021, J INTEGER SEQ, V24, P5
[6] On the multidimensional zeta functions associated with theta functions, and the multidimensional Appell polynomials
Bayad, Abdelmejid
Hajli, Mounir
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (05) : 2679 - 2694
[7] Beckwith D., 2014, AM MATH MON, V121, P267, DOI [DOI 10.4169/AMER.MATH.MONTHLY.121.03.266, https://doi.org/10.4169/amer.math.monthly.121.03.266]
[8] On the explicit formulas for zeta functions
Bouarroudj, Sofiane
Hajli, Mounir
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2020, 43 (17) : 10249 - 10261
[9] Alternating Convolutions of Catalan Numbers
Chu, Wenchang
[J]. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2022, 53 (01): : 95 - 105
[10] Debnath L., 2014, INTEGRAL TRANSFORMS, DOI DOI 10.1201/617670

← 1 2 3 4 →