Analytical and numerical aspects of a generalization of the complementary error function

作者：Deano Alfredo; Temme Nico M^*

来源：Applied Mathematics and Computation, 2010, 216(12): 3680-3693.

DOI：10.1016/j.amc.2010.05.025

• Complementary error function
• Singular perturbation problem
• Incomplete gamma function
• Confluent hypergeometric function
• Asymptotic expansions
• Recurrence relations

In this paper we discuss analytical and numerical properties of the function V(nu,mu)(alpha,beta,z) = integral(infinity)(0)e(-zt) (t + alpha)(nu) (t + beta)(mu)dt, with alpha, beta; Rz > 0, which can be viewed as a generalization of the complementary error function, and in fact also as a generalization of the Kummer U-function. The function V(nu,mu)(alpha, beta, z) is used for certain values of the parameters as an approximate in a singular perturbation problem. We consider the relation with other special functions and give asymptotic expansions as well as recurrence relations. Several methods for its numerical evaluation and examples are given.

• 出版日期2010-8-15