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Zbl 0749.65014
Lewanowicz, Stanisław
Evaluation of Bessel function integrals with algebraic singularities. (English)
[J] J. Comput. Appl. Math. 37, No.1-3, 101-112 (1991). ISSN 0377-0427

The author derives a new method for the numerical evaluation of the integral $\int\sp 1\sb 0(1-x)\sp \alpha x\sp \beta f(x)$ $J\sb \nu(ax)dx$. Here $\alpha$, $\beta$, $\nu$ and $a$ are given constants; $J\sb \nu$ is the Bessel function of the first kind and order $\nu$; $f$ is a sufficiently smooth function so that it can be expanded into a series of the shifted Jacobi polynomials. The proposed method is based on the series expansion for $J\sb \nu(ax)$.
[A.Laforgia (Potenza)]

MSC 2000:: *65D20 Computation of special functions
65D32 Quadrature formulas (numerical methods)
33C10 Cylinder functions, etc.

Keywords: Bessel function integrals with algebraic singularities; recurrence relations; shifted Jacobi polynomials; series expansion

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