The addition of Hypergeometric Series and a novel definition of the H function

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Published: Mar 1, 2025
DOI: https://doi.org/10.29070/1pw4sv31
Keywords:
H function, hypergeometric series, summation identity, special functions, mathematical analysis

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Authors

Akanksha Srivastava

Research Scholar, Department of Mathematics, Government Model Science College, Rewa, Madhya Pradesh

Dr. Neelam Pandey

Professor, Department of Mathematics, Government Model Science College, Rewa, Madhya Pradesh

Abstract

In this study, a new identity for the H function, which is a generalization of a number of special functions, is derived and its use in the summation of the hypergeometric series is discussed. The H function, which belongs to a class of rather wide functions, plays an immense role in complicated math problem solving throughout wide ranges of science and engineering. Thus, obtaining this new identity, we describe a more effective approach to the estimation of hypergeometric series which find numerous applications in combinatorics, physics, and mathematical analysis. The proposed identity reduces existing summation techniques into a single powerful tool for researchers using special functions. Also, this study contrasts the new identity with the conventional methods and demonstrates the superiority of the former in terms of computational efficiency and versatility. The results open the further development of theory of special functions and their usage for solving practical problems.

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Issue

Vol. 22 No. 1 (2025): Journal of Advances in Science and Technology (JAST)

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