Integral Representations and Zeros of the Lommel Function and the Hypergeometric 1F2 Function

We give different integral representations of the Lommel function s(mu,nu)(z) involving trigonometric and hypergeometric F-2(1) functions.By using classical results of Polya, we give the distribution of the zeros of s(mu,nu)(z) for certain regions in the plane (mu, nu). Further, thanks to a well known relation between the functions s(mu,nu)(z) and the hypergeometric F-1(2) function, we describe the distribution of the zeros of 1F2 for specific values of its parameters