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