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

Analytic evaluation of Gordon’s integral $${\mathrm{J}}_c^{j(\pm p)}(b,b^{\mathrm{\prime }};\lambda ,w,z)={\int }_0^{\mathrm{\infty }}{x}^{c+j-1}{e}^{-\lambda x}{}_1{F}_1(b;c;wx){}_1{F}_1(b^{\mathrm{\prime }};c\pm p;zx)dx,$$ 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.