A reduction formula for the hypergeometric function ₂F₂(β, 1/2; β+σ, −1/2; z) using finite-part integrals

Authors

Theodore M. Estadilla ⋅ PH National Institute of Physics, University of the Philippines Diliman
Eric A. Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

The hypergeometric function ₂F₂(β, 1/2; β+σ, −1/2; z) is shown to assume a finite-part integral representation, from which a reduction formula for ₂F₂ is obtained in terms of the confluent hypergeometric function ₁F₁. The result demonstrates how finite-part integrals can be used to uncover new relationships among the special functions of mathematical physics.

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Issue

2022: Proceedings of the 40th Samahang Pisika ng Pilipinas Physics Conference

Article ID

SPP-2022-PB-05

Section

Poster Session B (Complex Systems, Simulations, and Theoretical Physics)

Published

2022-09-27

How to Cite

[1]

TM Estadilla and EA Galapon, A reduction formula for the hypergeometric function 2F2(β, 1/2; β+σ, −1/2; z) using finite-part integrals, Proceedings of the Samahang Pisika ng Pilipinas 40, SPP-2022-PB-05 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-PB-05.