On the integral ∫10xν−1(1 − x)−λ lnmx dx

摘要

A recurrence relation is given for the integral in the title. Formulae which allow easy evaluation by symbolic algebra on a computer are given for integer and half-integer values of ν and λ. A comparison is made with formulae given in integral tables. Tables of explicit expressions for the above integral for small values of m, with ν = n, ν = n + 12, λ = l, and λ = l + 12 are also presented.