Generalized hypergeometric functions
著者
書誌事項
Generalized hypergeometric functions
Cambridge University Press, 1966 c2008
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注記
Bibliography: p. 255-268
Includes indexes
内容説明・目次
内容説明
The theory of generalized hypergeometric functions is fundamental in the field of mathematical physics, since all the commonly used functions of analysis (Besse] Functions, Legendre Functions, etc.) are special cases of the general functions. The unified theory provides a means for the analysis of the simpler functions and can be used to solve the more complicated equations in physics. The generalized Gauss function is also used in mathematical statistics and the basic analogues of the Gauss functions have applications in the field of number theory. Dr Slater's treatment leads on from a discussion of the Gauss functions to the basic hypergeometric functions, the hypergeometric integrals, bilateral series and Appel series. This book was planned jointly with the late Professor W. N. Bailey as an extended revision of his Cambridge Mathematical Tract (1935) on the subject and Dr Slater has continued it single-handed since Professor Bailey's death, incorporating in it the results of many of her own researches.
目次
- 1. The Gauss Function
- 2. The Generalized Gauss Function
- 3. Basic Hypergeometric Functions
- 4. Hypergeometric Integrals
- 5. Basic Hypergeometric Integrals
- 6. Bilateral Series
- 7. Basic Bilateral Series
- 8. Appell Series
- 9. Basic Appell Series.
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