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

Analytic evaluation of Gordon's integral $\operatorname {J}_c^{j(\pm p)}(b,b';λ,w,z)=\int_0^\infty x^{c+j-1}e^{-λx}{}_1F_1(b;c;wx){}_1F_1(b';c\pm p;zx)dx,$ 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.

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