RETRACTED ARTICLE: Approximation of analytic functions by bessel functions of fractional order

Abstract

We solve the inhomogeneous Bessel differential equation $$ {x^2}y''(x) + xy'(x) + \left( {{x^2} - {\nu^2}} \right)y(x) = \sum\limits_{m = 0}^\infty {{a_m}{x^m},} $$ where ν 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.