Functions and Analysis

    

Numerical Evaluation of Three Integrals of the Kind Int_0^oo X^m Dx/(1+x^n*sin^2 x)

Authors: Richard J. Mathar

Definite integrals along the real axis from zero to infinity with functions with denominator 1+x^n*sin^2 x suffer from dominant peaks at all x-values that are close to Pi, which impedes sampling the function with generic discrete numerical methods. We demonstrate the method of integrating along a closed contour around a circular sector in the complex x-plane and collecting the sum of all (infinitely many) residues inside the sector with an adapted series acceleration.

Comments: 11 Pages.

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Submission history

[v1] 2024-09-06 16:30:37

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