Inversion of the Struve transform of half integer order

Abstract

AbstractDefining a spherical Struve function we show that the Struve transform of half integer order, or spherical Struve transform,where n is a non-negative integer, may under suitable conditions be solved for f(t):where is the sum of the first n + 1 terms in the asymptotic expansion of φn(x) as x → ∞. The coefficients in the asymptotic expansion are identified asIt is further shown that functions φn (x) which are representable as spherical Struve transforms satisfy n + 1 integral constraints, which in turn allow the construction of many equivalent inversion formulae.