On the Asymptotic Approximation of Integrals
Copyright policy )On the Asymptotic Approximation of Integrals
This paper is concerned with an attempt to improve the accuracy of certain asymptotic approximations. The basic idea is simply to redefine the large parameter in a particular way. This idea is applied to four examples, including a Laplace integral, the gamma function, and an integral which can be treated by Erdélyi's method. In all cases there is a substantial improvement in accuracy.
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), gamma function, Laplace integral, asymptotic approximations, Gamma, beta and polygamma functions, Erdélyi's method
Asymptotic approximations, asymptotic expansions (steepest descent, etc.), gamma function, Laplace integral, asymptotic approximations, Gamma, beta and polygamma functions, Erdélyi's method
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