Asymptotic representations for hypergeometric-Bessel type function and fractional integrals

[摘要] The paper is devoted to the study of asymptotic relations for the function [GRAPHICS] generalising Tricomi confluent hypergeometric function and modified Bessel function of the third kind. The full asymptotic representations for lambda(gamma,sigma)((beta))(z) at zero and infinity are established. Applications are given to obtain full asymptotic expansions near zero and infinity for the Liouville fractional integral [GRAPHICS] and for the Erdelyi-Kober-type fractional integral [GRAPHICS] with beta > 0 and etais an element ofC of power-exponential function f(t), and for three other fractional integrals. (C) 2002 Elsevier Science B.V. All rights reserved.

[发布日期] 2002-12-15

[关键词] asymptotic expansions;confluent hypergeometric function;Bessel-type function;Liouville and Erdelyi-Kober-type fractional integrals