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