Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. For instance, Euler found the gamma function, which extends the factorial. The Bessel functions and Legendre polynomials play a role in three dimensions similar to the role of sine and cosine in two dimensions. This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials. The basic building block of the functions studied in this book is the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg’s multidimensional integrals, a number of important but relatively unknown nineteenth century results are included. The authors discuss Wilson’s beta integral and the associated orthogonal polynomials. Someq-extensions of beta integrals and of hypergeometric series are presented with Bailey chains employed to derive some results. An introduction to spherical harmonics and applications of special functions to combinatorial problems are included. The book also desls with finite field versions of some beta integrals.
The authors provide organizing ideas, motivation, and historical backgroud for the study and application of some important special functions. This clearly expressed and readable work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics.
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國外的數學一般寫作都用一點修辭和比喻,挺好玩的。真正講明白特殊函數2014.3.30:還是閱讀瞭小榖正雄的《特殊函數》,這本書裏有些過於呆闆和復雜的證明,我纔理解。其實關於歐拉函數的漸進展開完全可以放在最速下降法之後講完斯特林公式再講,本書的處理有點復雜化瞭;關於特殊函數的黎曼公式錶示,我一直沒有理解:其實要加入橢球坐標,再加入常微分方程的奇點理論,就ok
评分@2008-08-03 17:30:24
评分@2008-08-03 17:30:24
评分國外的數學一般寫作都用一點修辭和比喻,挺好玩的。真正講明白特殊函數2014.3.30:還是閱讀瞭小榖正雄的《特殊函數》,這本書裏有些過於呆闆和復雜的證明,我纔理解。其實關於歐拉函數的漸進展開完全可以放在最速下降法之後講完斯特林公式再講,本書的處理有點復雜化瞭;關於特殊函數的黎曼公式錶示,我一直沒有理解:其實要加入橢球坐標,再加入常微分方程的奇點理論,就ok
评分國外的數學一般寫作都用一點修辭和比喻,挺好玩的。真正講明白特殊函數2014.3.30:還是閱讀瞭小榖正雄的《特殊函數》,這本書裏有些過於呆闆和復雜的證明,我纔理解。其實關於歐拉函數的漸進展開完全可以放在最速下降法之後講完斯特林公式再講,本書的處理有點復雜化瞭;關於特殊函數的黎曼公式錶示,我一直沒有理解:其實要加入橢球坐標,再加入常微分方程的奇點理論,就ok
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