engleski

Convergence of generalized Kapteyn expansion

Series expansions of Kapteyn type in terms of Gamma function and a generalization of Bessel function of first kind were considered by Exton. Here we show that the convergence conditions given by him can be relaxed and the achieved results are optimal.

Bessel function of first kind $J_\nu(x)$; Hypergeometric function; Kapteyn series; Landau bounds for $J_\nu(x)$; Olenko's bound for $J_\nu(x)$.

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