The Gamma Function (Dover Books on Mathematics), by Emil Artin
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The Gamma Function (Dover Books on Mathematics), by Emil Artin
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This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, "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."Generations of teachers and students have benefitted from Artin's masterly arguments and precise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines functions, the Euler integrals and the Gauss formula, large values of x and the multiplication formula, the connection with sin x, applications to definite integrals, and other subjects.
The Gamma Function (Dover Books on Mathematics), by Emil Artin- Amazon Sales Rank: #682286 in Books
- Brand: Artin, Emil/ Butler, Michael (TRN)
- Published on: 2015-03-18
- Released on: 2015-02-18
- Original language: English
- Number of items: 1
- Dimensions: 8.70" h x .20" w x 5.80" l, .0 pounds
- Binding: Paperback
- 48 pages
From the Back Cover
This brief monograph on the gamma function was designed by the author to fill what he perceived as a gap in the literature of mathematics, which often treated the gamma function in a manner he described as both sketchy and overly complicated. Author Emil Artin, one of the twentieth century's leading mathematicians, wrote in his Preface to this book, "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."Generations of teachers and students have benefitted from Artin's masterly arguments and precise results. Suitable for advanced undergraduates and graduate students of mathematics, his treatment examines functions, the Euler integrals and the Gauss formula, large values of x and the multiplication formula, the connection with sin x, applications to definite integrals, and other subjects.Dover (2015) republication of the edition originally published by Holt, Rinehart & Winston, Inc., New York, 1964.See every Dover book in print atwww.doverpublications.com
About the Author
One of the 20th century's most prominent mathematicians, Emil Artin (1898–1962) taught at the University of Hamburg from 1923 to 1937. After emigrating to the United States, he taught at Notre Dame (1937–38), Indiana University (1938–46), and Princeton (1946–58) before returning to Hamburg in 1958. Dover also publishes his Galois Theory.
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Most helpful customer reviews
5 of 5 people found the following review helpful. An Intuitive Approach to the Gamma Function By jerbearmy This book is a quick, solid overview of the gamma function, which is the natural extension of the factorial function to arbitrary real (and complex) numbers. The gamma function is often quickly covered in advanced calculus and complex analysis courses, but in such cases the author usually just states and proves (or leaves to the exercises) the properties of gamma, leaving the student to wonder "where" these results come from.This book is unique in that it does not begin with gamma itself, but with convex and log-convex functions. It then proves that up to normalization, gamma is the only log-convex function satisfying the equation T(x+1) = xT(x). It then uses this characterization to motivate and prove the other well-known properties of gamma, such as Stirling's formula or the multiplication formula. For a reader whose background is not in classical analysis (my background is in operator algebras), it was very illuminating to see how a seemingly simple property like log-convexity could be used to systematically generate such results.Is a 38 page book worth $9? That's up to you. If you are just interested in knowing the properties of gamma, you likely have a list of them in another book on your shelf. But if you are interested to see "why" these results are true rather than only "proving" them, this book is a nice resource. As a mathematician who is trying to expand his classical analysis bag of tricks, I certainly do not regret this purchase.
0 of 0 people found the following review helpful. Amazing Book! By Jason Tesar This is an amazing book. If you want to learn everything about the gamma function, the advanced stuff made understandable, this is the book for you. His derivation of the multiplication formula is outstanding, relying on the true definition of the gamma function which he explains very well and leads up to the theorem.
0 of 0 people found the following review helpful. Excellent By Dr. Charles Saunders Only a few pages but worth every cent if you have ever wanted to really understand the Gamma function.
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