On W. Gordon's integral (1929) and related identities

Abstract

Analytic evaluation of Gordon's integral $$J_c^{j(\pm p)}(b,b^{\prime };\lambda ,w,z)={\int }_0^{\infty }{x}^{c+j-1}{e}^{-\lambda x}{}_1{F}_1(b;c;wx){}_1{F}_1(b^{\prime };c\pm p;zx)dx,$$ are given along with convergence conditions. It shows enormous number of definite integrals, frequently appear in theoretical and mathematical physics applications, easily deduced from this generalized integral.

14 pages

References in corpus (1)

• Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials