A Reduction Formula

In this paper I construct a reduction formula for the integral the formula connects any three consecutive members of a set I 0 , I 1 , I 2 , …, I m . We regard m as given, and, in order to avoid wasting time over trivialities, we postulate that the constants a, α, β, γ δ (which are not restricted to be real) have real parts large enough to ensure (i) that the integrals I n under consideration and the integrals related to them which will be introduced subsequently are all absolutely convergent, and (ii) that, in all the partial integrations which will be effected, the integrated parts vanish at both limits.