Titlebook: Series of Bessel and Kummer-Type Functions; Árpád Baricz,Dragana Jankov Maširević,Tibor K. Pog Book 2017 Springer International Publishing

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Book 2017pecial functions, such as Struve and von Lommel functions. The aim is also to find the coefficients of the Neumann and Kapteyn series, as well as closed-form expressions and summation formulas for the series of Bessel functions considered. Some integral representations are deduced using techniques f

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Neumann Series,ified Bessel functions of the first and second kind. In order to achieve our goal we use several methods: the Euler–Maclaurin summation technique, differential equation technique, fractional integration technique. Moreover, we present some interesting results on the coefficients of Neumann series, p

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,Schlömilch Series,functions of the second kind. Closed expressions for some special Schlömilch series together with their connection to Mathieu series are also investigated. The chapter ends with an integral representation formula for number theoretical summation by Popov, which also covers the theta-transform identi

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Miscellanea,nctions family (Bessel functions of the first and second kind, modified Bessel functions of the first and second kind, Struve functions, modified Struve functions etc.). In Sects. 5.7–5.9 we consider Dini series and Jacobi polynomials, respectively. Next section is devoted to summations of Schlömilc

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,Schlömilch Series,ated. The chapter ends with an integral representation formula for number theoretical summation by Popov, which also covers the theta-transform identity coming from functional equation for the Epstein Zeta function.