Abstract
This paper is motivated by an open problem of several inequalities for confluent hypergeometric functions. We give some inequalities for simple Laguerre, Laguerre, pseudo-Laguerre, Shively’s pseudo-Laguerre, and Hermite functions of one and two variables.
Highlights
Inequalities for the special functions appear infrequently in the literature
Inequalities for the ratio of confluent hypergeometric functions are available in the literature
The author has earlier studied the inequalities for Humbert functions [ ]
Summary
Inequalities for the special functions appear infrequently in the literature. Some of these inequalities are closely related to those presented here. We define the simple Laguerre function of two variables by Similar investigations are developed to establish new inequalities for a simple Laguerre function of two variables. We discuss some inequalities for classical Laguerre functions of one and two variables.
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