The Gamma Function (Dover Books on Mathematics)

This book about the gamma function is intended to be read by professional mathematicians. It is not for people who merely have an interest in mathematics. At the time it was published it had several insights about the gamma function that were not so common in the literature. However, most of them seem to have made it into the mainstream literature by now. I think everything in this book, I've been able to learn from my various books on analytic number theory.

a classic. Artin's books are blessed with remarkable, revealing, but simple exposition. the book is terse, but cuts to the heart of what the gamma function is and how it behaves. i especially liked its treatment of convexity under the limit operation. i have not found comparable exposition online or in other texts in regards to this.

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.

Only a first course in calculus is needed to understand this book. Theorems are explained step by step. The veil on some of the most intimidating gamma identities is stripped away as the author methodically develops the formula, and the reader finishes with a greater confidence in dealing with this important function.

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.

I bought the book to review its approach to the asymptotic behavior of the gamma function.

Emil Artin relies on coneptual approaches to illuminating the gamma function's features instead of tedioius calculations. This book requires little more than calculus for its background. I highly recommend any of Artin's books as they are some of the best exposition you can find on the subjects he writes about.

This one comes as close to a great classic as any book you will read. Quite engaging, thorough, and a joy to read. You usually can't go wrong with these Dover books. They are reprints from the best classics. However, being such, they can use a slightly different terminology and approach to a topic. Which is exactly what I love about them. You are getting the theory right from the "horse's mouth," so to speak. A modern text can sometimes hide the motivation behind an important topic and leave an initiate feeling like you're just "manipulating symbols" without a clear grasp of the WHY. I don't think you can find a better treatment on the Gamma function (one of the most useful), or which is more enjoyable to read. Be careful if it is your first introduction to the topic. Better first pick up the notion from a modern calculus textbook.

Es un excelente libro sobre la función gamma aun cuando su tamaño es muy pequeño, trata puntos muy específicos que en otros libros no se tratan.

終わりの方で、フーリエ級数の話が出てきます。「級数sinx/1+sin2x/2+sin3x/3+・・・は、ｘ≠πｎで一様収束」等、僕は全く知らなかったのですが、逆に、そういう事が縁で、こちらの方面に魅せられました。将に「蒙を啓かれた」感。

O livro é na verdade uma monografia escrita pelo grande matemático suiço Emil Artin, ainda na primeira metade do século passado. A obra começa falando sobre funções convexas no primeiro capítulo, sendo um assunto que para mim, leigo sobre função gama, não me interessou num primeiro instante. O segundo capítulo é o que realmente importa para aqueles que, como eu, desejam saber como se dá a ligação entre a função fatorial e a função Gama, já que a segunda é uma generalização da primeira. E isso é esclarecido de forma curta e direta já no primeiro parágrafo e primeira equação do capítulo 2. Portanto, se você é um leigo completo nessa parte da matemática e deseja matar logo a curiosidade, além de aprender um pouco mais sobre essa função (descrita primeiramente pelo grande matemático Leonhard Euler), aconselho iniciar a leitura a partir do segundo capítulo, para depois ler o resto. Obra recomendada!

veru good

Very effective treatise on convexity and its consequences. Useful as a side tool, for the study of the Riemann Zeta function.