2019
Том 71
№ 9

# Approximation of analytic functions by Bessel functions of fractional order

Jung S.-M.

Abstract

We solve the inhomogeneous Bessel differential equation $$x^2y''(x) + xy'(x) + (x^2 - \nu^2)y(x) = \sum^{\infty}_{m=0} a_mx^m$$, where $\nu$ is a positive nonintegral number, and use this result for the approximation of analytic functions of a special type by the Bessel functions of fractional order.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 12, pp 1641-1659.

Citation Example: Jung S.-M. Approximation of analytic functions by Bessel functions of fractional order // Ukr. Mat. Zh. - 2011. - 63, № 12. - pp. 1699-1709.

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