Indefinite integrals of special functions from integrating factors

ABSTRACT

Some general integrals are presented which were obtained from two integrating factors $f\left(x\right)$ and $\hat{f}\left(x\right)$ for the first two and last two terms, respectively, of the second-order linear ordinary differential equation obeyed by many special functions. The integrating factor $f\left(x\right)$ is identical to the Lagrangian factor introduced in Conway [A Lagrangian method for deriving new indefinite integrals of special functions. Integral Transforms Spec Funct. 2015;26(10):812–824; Indefinite integrals of some special functions from a new method. Integral Transforms Spec Funct. 2015;26(11):845–858] and sometimes provides textbook integrals. The integrals provided by the second factor seem to have been little explored. Results are given for Gauss hypergeometric functions and Kummer confluent hypergeometric functions. All results presented have been checked using Mathematica.

KEYWORDS:

• Differential equations
• Gauss hypergeometric function
• Kummer function

AMS SUBJECT CLASSIFICATIONS:

• 34B30
• 33C05
• 33C15

Disclosure statement

No potential conflict of interest was reported by the author.