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Calculation of improper integrals on polar axis \(r\geq R_0>0\) by means of Kontorovich-Lebedev-Legendre integral transforms. (Ukrainian. English summary) Zbl 0953.44002

Summary: A family of improper multiparametric integrals on adjoint Legendre functions and modified Bessel functions is calculated by means of Kantorovich-Lebedev-Legendre integral transforms.

MSC:

44A20 Integral transforms of special functions
44A15 Special integral transforms (Legendre, Hilbert, etc.)
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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