ON A FUNCTION ASSOCIATED WITH THE LOGARITHMIC DERIVATIVE OF THE GAMMA FUNCTION

Abstract

The function ψ(k)—log k+1/2k is real for real positive k, and complex for pure imaginary k, its imaginary part being then given by a simple formula. Its real part, considered as a function of 1/k², varies smoothly through 1/k² = 0, and is a convenient auxiliary function to use for interpolation purposes; it is also required in connexion with the tabulation of the confluent hypergeometric function.

The real part of ψ(k)—log k+1/2k has been evaluated, and is tabulated, as a function of 1/k² for the range 1/k² − 1.00(0.01)+1.00, to 8 decimals.