RESEARCH PAPER INTEGRAL EXPRESSIONS FOR MATHIEU–TYPE POWER SERIES AND FOR THE BUTZER–FLOCKE–HAUSS Ω–FUNCTION ˇ Zivorad Tomovski 1 and Tibor K. Pog´ any 2 Abstract Dedicated to Professor Peter K. Rusev on the occasion of his 80th birthday In this paper several integral representations for the generalized frac- tional order Mathieu type power series S μ (r; x)= ∞  n=1 2nx n (n 2 + r 2 ) μ+1 ( r ∈ R,μ> 0, |x|≤ 1 ) are presented. Also new integral expressions are derived for the Butzer– Flocke–Hauss (BFH) complete Omega function. MSC 2010 : Primary 33E20, 40A10; Secondary 33C10, 33C20, 44A20 Key Words and Phrases: generalized Mathieu series, alternating gen- eralized Mathieu series, Fourier sine transform, Bessel function of the first kind, Butzer–Flocke–Hauss (BFH) Ω–function, Fox–Wright generalized hy- pergeometric function, confluent hypergeometric function c  2011 Diogenes Co., Sofia pp. 623–634 , DOI: 10.2478/s13540-011-0036-2