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Mellin's Formula

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(e^(ypsi_0(x))Gamma(x))/(Gamma(x+y))=product_(n=0)^infty(1+y/(n+x))e^(-y/(n+x)),

where psi_0(x) is the digamma function and Gamma(x) is the gamma function.

See also

Digamma Function, Gamma Function, Infinite Product

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References

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, p. 6, 1981.

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Mellin's Formula

Cite this as:

Weisstein, Eric W. "Mellin's Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MellinsFormula.html

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