gamma function

Do you remember anything at all about the gamma function?"

The integral on the right hand side may be recognized as the gamma function.

Up to elementary factors, it is a special case of the double gamma function.

A good solution to this is the gamma function.

The gamma function is defined for all complex numbers.

It is somewhat problematic that a large number of definitions have been given for the gamma function.

See Particular values of the gamma function for calculated values.

However, the gamma function does not appear to satisfy any simple differential equation.

The Gamma function is an important special function in mathematics.

A definite and generally applicable characterization of the gamma function was not given until 1922.

A thorough and systematic book devoted entirely to the subject of the gamma function.

We can rewrite the above in terms of the Gamma function:

Other efficient series for Z(t) are known, in particular several using the incomplete gamma function.

Thus, the gamma function can be evaluated to "N" bits of precision with the above series.

Here, the new factor is proportional to a quotient of gamma functions.

When is an integer, the Gamma function can be computed explicitly.

This is another way of denoting the gamma function.

The incomplete gamma function is a special case.

Thus, the gamma function may now be defined as:

These functional equations are satisfied by the gamma function.

For the explicit case of the gamma function, the identity is a product of values; thus the name.

The gamma function can be seen as a solution to the following interpolation problem:

The formula is therefore feasible for arbitrary-precision evaluation of the gamma function.

The derivative of the upper incomplete gamma function with respect to "x" is well known.

In the words of Davis, "each generation has found something of interest to say about the gamma function.