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Special functions /
"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 functio...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK ; New York, NY, USA :
Cambridge University Press,
1999.
|
| Colección: | Encyclopedia of mathematics and its applications ;
v. 71. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 1.12 The p-adic Gamma FunctionExercises; 2 The Hypergeometric Functions; 2.1 The Hypergeometric Series; 2.2 Euler's Integral Representation; 2.3 The Hypergeometric Equation; 2.4 The Barnes Integral for the Hypergeometric Function; 2.5 Contiguous Relations; 2.6 Dilogarithms; 2.7 Binomial Sums; 2.8 Dougall's Bilateral Sum; 2.9 Fractional Integration by Parts and Hypergeometric Integrals; Exercises; 3 Hypergeometric Transformations and Identities; 3.1 Quadratic Transformations; 3.2 The Arithmetic-Geometric Mean and Elliptic Integrals; 3.3 Transformations of Balanced Series
- 3.4 Whipple's Transformation3.5 Dougall's Formula and Hypergeometric Identities; 3.6 Integral Analogs of Hypergeometric Sums; 3.7 Contiguous Relations; 3.8 The Wilson Polynomials; 3.9 Quadratic Transformations
- Riemann's View; 3.10 Indefinite Hypergeometric Summation; 3.11 The W-Z Method; 3.12 Contiguous Relations and Summation Methods; Exercises; 4 Bessel Functions and Confluent Hypergeometric Functions; 4.1 The Confluent Hypergeometric Equation; 4.2 Barnes's Integral for 1F1; 4.3 Whittaker Functions; 4.4 Examples of 1F1 and Whittaker Functions; 4.5 Bessel's Equation and Bessel Functions
- 4.6 Recurrence Relations4.7 Integral Representations of Bessel Functions; 4.8 Asymptotic Expansions; 4.9 Fourier Transforms and Bessel Functions; 4.10 Addition Theorems; 4.11 Integrals of Bessel Functions; 4.12 The Modified Bessel Functions; 4.13 Nicholson's Integral; 4.14 Zeros of Bessel Functions; 4.15 Monotonicity Properties of Bessel Functions; 4.16 Zero-Free Regions for 1F1 Functions; Exercises; 5 Orthogonal Polynomials; 5.1 Chebyshev Polynomials; 5.2 Recurrence; 5.3 Gauss Quadrature; 5.4 Zeros of Orthogonal Polynomials; 5.5 Continued Fractions; 5.6 Kernel Polynomials