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Emil Artin, “The Gamma Function” 
1964 | pages: 39 | ASIN: B0006BMA10 | PDF | 3,2 mb

 

“I have written this monograph with the hope of filling in a certain gap which has often been felt to exist in the mathematical literature. Despite the importance of the gamma function in many different parts of mathematics, calculus books often treat this function in a very sketchy and complicated fashion. I feel that this monograph will help to show that the gamma function can be thought of as one of the elementary functions, and that all of its basic properties can be established using elementary methods of the calculus. 
As far as prerequisites are concerned, the reader need only be well acquainted, with calculus, including improper integrals. Some of the more important concepts needed will even be introduced and discussed again in the first chapter. With this background the reader should have no trouble understanding everything but the later parts of the last two chapters, which do assume some knowledge of Fourier series. But then, these parts of the monograph can be passed over on a first reading without any difficulty whatsoever.” – Emil Artin.

 

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