Four Families of Summation Formulas for 4F3(1) with Application

A collection of functions organized according to their indexing based on non-negative integers is grouped by the common factor of fixed integer N. This grouping results in a summation of N series, each consisting of functions partitioned according to this modulo N rule. Notably, when N is equal to t...

Full description

Saved in:
Bibliographic Details
Published in:Axioms 2024-03, Vol.13 (3), p.164
Main Authors: Kumar, Belakavadi Radhakrishna Srivatsa, Rathie, Arjun K., Choi, Junesang
Format: Article
Language:English
Subjects:
beta function
gamma function
Gauss’s summation formula 2F1
generalized hypergeometric series
Hypergeometric functions
integral formulas
Integrals
Kummmer’s summation formula 2F1(−1)
Numbers
Partitioning
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A collection of functions organized according to their indexing based on non-negative integers is grouped by the common factor of fixed integer N. This grouping results in a summation of N series, each consisting of functions partitioned according to this modulo N rule. Notably, when N is equal to two, the functions in the series are divided into two subseries: one containing even-indexed functions and the other containing odd-indexed functions. This partitioning technique is widely utilized in the mathematical literature and finds applications in various contexts, such as in the theory of hypergeometric series. In this paper, we employ this partitioning technique to establish four distinct families of summation formulas for F34(1) hypergeometric series. Subsequently, we leverage these summation formulas to introduce eight categories of integral formulas. These integrals feature compositions of Beta function-type integrands and F23(x) hypergeometric functions. Additionally, we highlight that our primary summation formulas can be used to derive some well-known summation results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13030164