On the integral ∫∞0 χv−1(1 + βχ)−λlnmχ dχ

摘要

A recurrence relation is given for the integral in the title. Formulae which allows easy evaluation by formula manipulation on a computer are given for integer and half-integer values of v and λ. A comparison with formulae given in integral tables is made. Using results obtained, four infinite series are expressed in closed form, generalizing well-known results for infinite series of reciprocal powers. Tables of explicit expressions for the above integral for small values of m, with v = n, v = n + 12, λ = l, λ = l + 12, and certain values of β, are also presented.