Approximation of analytic functions by Bessel functions of fractional order - Jung, S.-M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
We solve the inhomogeneous Bessel differential equation$$x^2y''(x) + xy'(x) + (x^2 - u^2)y(x) = \sum^{∞}_{m=0} a_mx^m$$,where $ u$ 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.