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A note on the logarithmic derivative of the gamma function

Published online by Cambridge University Press:  31 October 2008

A. P. Guinand
A. P. Guinand
Affiliation:
Military College of Science, Shrivenham.
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The object of this note is to give simpler proof* of two formulae involving the function ψ (z) which I have proved elsewhere by more complicated methods.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 38 , January 1952 , pp. 1 - 4
Copyright
Copyright © Edinburgh Mathematical Society 1952

References

1 Journal London Math. Soc., 38 (1947), 14–18.Google Scholarψ(z) denotes Γ′ (z) / Γ (z).

2 The first formula shows that ψ(x + 1) – log x is self-reciprocal with respect to the Fourier cosine kernel 2 cos 2πx. It is strange that this result should have been overlooked, but I can find no trace of it.

Cf. Mehrotra, B. M., Journal Indian Math. Soc. (New Series), 38 (1934), 209–27Google Scholar for a list of self-reciprocal functions and references.

3 Stewart, C. A., Advanced. Calculus, (London, 1940), 495 and 497.Google Scholar

1 Stewart, C. A., loc cit. 457.Google Scholar

2 Stewart, C. A., loc. cit. 504.Google Scholar

1 Whittaker, E. T. and Watson, G. N., Modern Analysis (Cambridge, 1927), 278.Google Scholar

2 Stewart, C. A., loc. cit. 505.Google Scholar