Indefinite integrals from Wronskians for Whittaker and Gauss hypergeometric functions

Abstract

A method related to Wronskians has recently been applied to derive many indefinie integrals involving Bessel functions and associated Legendre functions. Here the same method is applied to derive indefinite integrals of Whittaker functions and Gauss hypergeometric functions. All the integrals presented here appear to be new and are derived either directly from Wronskians or from a differential equation related to Wronskians. All the results presented have been checked numerically using Mathematica.

Keywords:

• Differential equations
• Whittaker functions
• Gauss hypergeometric functions
• incomplete beta functions

AMS Subject Classifications:

• 34B30
• 33C15
• 33C05
• 33B20
• 35A24

Disclosure statement

No potential conflict of interest was reported by the author.