RETRACTED ARTICLE: Approximation of analytic functions by bessel functions of fractional order

We solve the inhomogeneous Bessel differential equation\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {x^2}y''(x) + xy'(x) + \left( {{x^2} - {\nu^2}} \right)y(x) = \sum\limits_{m = 0}^\infty {{a_m}{x^m},} $$\end{document}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.