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Gauss Multiplication Formula

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For a positive integer n,

(2pi)^((n-1)/2)n^(1/2-nz)Gamma(nz)=product_(k=0)^(n-1)Gamma(z+k/n),

See also

Gamma Function, Legendre Duplication Formula, Polygamma Function

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References

Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 256, 1972.Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, pp. 4-5, 1981.

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Gauss Multiplication Formula

Cite this as:

Weisstein, Eric W. "Gauss Multiplication Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GaussMultiplicationFormula.html

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