Gamma function

Gamma function is an extension of the factorial function for real numbers. In x=0 and negative integer values gamma function has poles. For positive real x or negative non-integer x gamma function is

For positive integer x Γ(n)=(n-1)!

It should be noted that these formula is applicable for the complex argument too. But the gamma function of the complex argument is seldom used, so the algorithm in this module operates with real arguments only. Of course, the integration is not an effective way for gamma function calculation. Instead, it is used as a series of formulas to bring an argument to [2,3] interval in which the rational approximation is built. For big x (more than 33) Stirling's formula is used. This algorithm is implemented in the Gamma subroutine.

Gamma function can possess very big values, so it is often used as a logarithm of the gamma function, which can be calculated by using the LnGamma subroutine.

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