Integral representations of the derivatives of the Gauss hypergeometric function with respect to its parameters

Authors

  • Lloyd Llena Villanueva ⋅ PH National Institute of Physics, University of the Philippines Diliman
  • Eric A. Galapon ⋅ PH National Institute of Physics, University of the Philippines Diliman

Abstract

We derive a generalized expression of the derivatives of the Gauss hypergeometric function with respect to its parameter by introducing an auxiliary function and performing some operations. The obtained expression involves infinite series that is only analytic inside the unit circle |z| = 1. Using the concept of analytic continuation, we obtain an integral representation of the derivatives of the Gauss hypergeometric function that is analytic in the whole complex plane, except at its singularities.

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Issue

Article ID

SPP-2021-PC-11

Section

Poster Session C (Theoretical and Mathematical Physics)

Published

2021-09-29

How to Cite

[1]
LL Villanueva and EA Galapon, Integral representations of the derivatives of the Gauss hypergeometric function with respect to its parameters, Proceedings of the Samahang Pisika ng Pilipinas 39, SPP-2021-PC-11 (2021). URL: https://proceedings.spp-online.org/article/view/SPP-2021-PC-11.