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

In this paper we discuss analytical and numerical properties of the function V�,µ(α, β, z) = R 1 0 e zt (t + α) � (t + β) µ dt, with α, β, 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�,µ(α, β, z) is used for certain values of the parameters as an approximant 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. 2000 Mathematics Subject Classification: 33B20, 33C15, 41A60, 65D20, 65Q05.

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