Inequalities for Laguerre functions

Abstract

The main published inequality for Laguerre functions Lvμ(z) seems to be for Laguerre polynomials Ln0(x) only; it is [2: 10.18(3)]: |Ln(x)|≤ex/2  for  x>0.This paper presents several inequalities for Laguerre polynomials Lnμ(x) and Laguerre functions Lvμ(x), most of which do not seem to be in the existing literature. The corresponding inequalities for confluent hypergeometric functions are noted.

Keywords

• Laguerre polynomial; Laguerre function; confluent hypergeometric function; fractional integration.