engleski

New integral forms of generalized Mathieu series and related applications

The main object of this article is to present a systematic study of integral representations for generalized Mathieu series and its alternating variant, and to derive a new integral expression for these special functions by contour integration using rectangular integration path. Also, by virtue of newly established integral form of generalized Mathieu series, we obtain a new integral expression for the Bessel function of the first kind of half integer order, solving a related Fredholm integral equation of the first kind with nondegenerate kernel.

Mathieu and generalized Mathieu series; Integral representation of series; Bessel function of the first kind; Fredholm integral equation of the first kind; Mellin transform.

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