21. Further, \ Gamma is the gamma function . 22. The formula is therefore feasible for arbitrary-precision evaluation of the gamma function . 23. Where \ Gamma is the Euler gamma function . 24. The gamma function is defined for all complex numbers except the non-positive integers. 25. In fact the gamma function corresponds to the Mellin transform of the negative exponential function: 26. A definite and generally applicable characterization of the gamma function was not given until 1922. 27. They can be expressed in terms of higher order poly-gamma functions as follows: 28. Many math packages allow you to compute Q, the regularized gamma function , directly. 29. Thus, the gamma function can be evaluated to bits of precision with the above series. 30. One way to prove would be to find a differential equation that characterizes the gamma function .
