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The Quarterly Journal of Mechanics and Applied Mathematics 1948 1(1):29-34; doi:10.1093/qjmam/1.1.29
© 1948 by Oxford University Press
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ON A FUNCTION ASSOCIATED WITH THE LOGARITHMIC DERIVATIVE OF THE GAMMA FUNCTION

D. R. HARTREE and S. JOHNSTON

( Cavendish Laboratory Cambridge
Manchester )

The function {psi}(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 {psi}(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.


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