| 41. | An elegant and deep application of the gamma function is in the study of the Riemann zeta function.
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| 42. | Thus this normalization makes it clearer that the gamma function is a continuous analogue of a Gauss sum.
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| 43. | :The continuity of the relationship between the gamma function and factorial recquires that 0 ! = 1.
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| 44. | Integrals of such expressions can occasionally be solved in terms of the gamma function when no elementary solution exists.
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| 45. | Where is the gamma function, which is an equality of meromorphic functions valid on the whole complex plane.
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| 46. | For negative integer power k, the gamma function is undefined and we have to use the following relation:
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| 47. | In 1919, Ramanujan ( 1887 1920 ) used properties of the Gamma function to give a simpler proof.
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| 48. | Similarly, the upper incomplete gamma function is defined as an integral from a variable lower limit to infinity.
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| 49. | The one may be converted to the other by making use of the integral representation of the Gamma function:
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| 50. | Kinkelin's works dealt with the gamma function, infinite series, and solid geometry of the axonometric.
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