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Some properties of the gamma function including Stirling's formula
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- Authors
- Advisor
- Kim Young-One
- Major
- 자연과학대학 수리과학부
- Issue Date
- 2013-02
- Publisher
- 서울대학교 대학원
- Description
- 학위논문 (석사)-- 서울대학교 대학원 : 수리과학부, 2013. 2. 김영원.
- Abstract
- The gamma function, introduced by the Swiss mathematician Leonhard Euler (1707-1783), plays a central role in modern mathematics. This remarkable brainchild
was a result of generalizing the factorial to non integer values. Afterward, because of its great importance, it was discovered by great mathematicians as well as many
others.
The aim of this work is to give meticulous proofs of several important known properties of the gamma function. We start by defining gamma function as an integral form and it is extended by analytic continuation to all complex numbers except the non-positive integers, yielding a meromorphic function we henceforth continue to call the gamma function. After describing several important results of gamma function, we finalize our work with obtaining the Stirling's formula to observe the behavior of the gamma function for large values inasmuch as it indeed grows rapidly - faster than exponential function.
- Language
- English
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