engleski

Integral expressions for Mathieu-type power series and for the Butzer-Flocke-Hauss Ω-function

In this paper several integral representations for the Mathieu type power series \[ S_\mu(r ; x) = \sum_{; ; k=1}; ; ^{; ; \infty}; ; \frac{; ; 2k x^k}; ; {; ; (k^2+r^2)^{; ; \mu +1}; ; }; ; \qquad r\in \mathbb R, |x|\le 1 \] are presented. Also new integral expressions are derived for the Butzer-Flocke-Hauss (BFH) complete Omega function.

Generalized Mathieu series; Alternating generalized Mathieu series; Fourier sine transform; Bessel function of the first kind; Fox-Wright generalized hypergeometric function; Butzer-Flocke-Hauss (BFH) Omega-function; Confluent hypergeometric function

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