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The reciprocal is sometimes used as a starting point for numerical computation of the gamma function, and a few software libraries provide it separately from the regular gamma function. Karl Weierstrass called the reciprocal gamma function the "factorielle" and used it in his development of the Weierstrass factorization theorem .
The gamma function then is defined in the complex plane as the analytic continuation of this integral function: it is a meromorphic function which is holomorphic except at zero and the negative integers, where it has simple poles. The gamma function has no zeros, so the reciprocal gamma function 1 / Γ(z) is an entire function.
A fair amount of effort has been made to calculate the numerical value of the Fransén–Robinson constant with high accuracy. The value was computed to 36 decimal places by Herman P. Robinson using 11 point Newton–Cotes quadrature, to 65 digits by A. Fransén using Euler–Maclaurin summation, and to 80 digits by Fransén and S. Wrigge using Taylor series and other methods.
In probability theory and statistics, the inverse gamma distribution is a two-parameter family of continuous probability distributions on the positive real line, which is the distribution of the reciprocal of a variable distributed according to the gamma distribution.
The gamma function is an important special function in mathematics.Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general.
a partial charge. δ− represents a negative partial charge, and δ+ represents a positive partial charge chemistry (See also: Solvation) the chemical shift of an atomic nucleus in NMR spectroscopy. For protons, this is relative to tetramethylsilane = 0; stable isotope compositions; declination in astronomy; noncentrality measure in statistics [7]
The inverse gamma function also has the following asymptotic formula [7] + ( ()), where () is the Lambert W function. The formula is found by inverting the Stirling approximation , and so can also be expanded into an asymptotic series.
In Bayesian inference, the gamma distribution is the conjugate prior to many likelihood distributions: the Poisson, exponential, normal (with known mean), Pareto, gamma with known shape σ, inverse gamma with known shape parameter, and Gompertz with known scale parameter.