| 31. | When and are positive integers, it follows from the definition of the gamma function that:
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| 32. | Complex analysis shows how properties of the real incomplete gamma functions extend to their holomorphic counterparts.
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| 33. | Where the numerator is the upper incomplete gamma function and the denominator is the gamma function.
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| 34. | Where the numerator is the upper incomplete gamma function and the denominator is the gamma function.
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| 35. | *In general, you have to calculate the Gamma function for the argument plus one.
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| 36. | In general, when computing values of the gamma function, we must settle for numerical approximations.
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| 37. | C . H . Brown derived rapidly converging infinite series for particular values of the gamma function:
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| 38. | Where B ( ) is the Beta function and \ Gamma ( ) is the Gamma function.
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| 39. | Which is an entire function, defined for every complex number, just like the reciprocal gamma function.
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| 40. | We can replace the factorial by a gamma function to extend any such formula to the complex numbers.
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