Binet's Log Gamma Formulas

Binet's first formula for the log gamma function lnGamma(z), where Gamma(z) is a gamma function, is given by


for R[z]>0 (Erdélyi et al. 1981, p. 21; Whittaker and Watson 1990, p. 249).

Binet's second formula is


for R[z]>0 (Erdélyi et al. 1981, p. 22; Whittaker and Watson 1990, pp. 250-251).

See also

Gamma Function, Log Gamma Function, Malmstén's Formula, Stirling's Approximation

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Erdélyi, A.; Magnus, W.; Oberhettinger, F.; and Tricomi, F. G. Higher Transcendental Functions, Vol. 1. New York: Krieger, 1981.Whittaker, E. T. and Watson, G. N. "Binet's First Expansion for logGamma(z) in Terms of an Infinite Integral" and "Binet's Second Expression for logGamma(z) in Terms of an Infinite Integral." §12.31 and 12.32 in A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, pp. 248-251, 1990.

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Binet's Log Gamma Formulas

Cite this as:

Weisstein, Eric W. "Binet's Log Gamma Formulas." From MathWorld--A Wolfram Web Resource.

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