Solution of integral equations of the first kind with a generalized hypergeometric function as kernel (Q759957)

The authors give the solutions of an integral equation of the first kind on (0,\(\infty)\), viz. \[ (*)\quad \int^{\infty}_{0}f(x)K(xy)dx=F(y), \] whose kernel K(xy) is a generalized hypergeometric function \(K(x)=_ mF_ n(\alpha_ 1,...,\alpha_ m;\beta_ 1,...,\beta_ n;-x),\) F(y) is a given function and f(x) is the unknown function, for the cases \(m=k\) and \(n=k+1\), \(m=k=n\), and \(m=k+1\) and \(n=k\). They give also three tables of kernels K(x) of (*) for some special functions and their corresponding functions, details of which are cited in the paper.