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