Special Functions / George E Andrews;
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TextPublisher number: :International Book Distributors | :Flat No 17, Prakash Apartment 4405/2, 5 Ansari Road Darya Ganj New Delhi Publication details: USA Cambridge University Press, 1999Description: xvi, 664p. 24cmISBN: 9780521789882Subject(s): Mathematics | Analysis | Functions, Special | Fonctions spéciales | Mathematics -- Calculus | Spezielle Funktion | Mathematics Mathematical Analysis | Spezielle FunktionDDC classification: 515.5 AND | Item type | Current library | Call number | Status | Notes | Date due | Barcode | Item holds |
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Books
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SNU LIBRARY | 515.5 AND (Browse shelf(Opens below)) | Not For Loan | Books Shifted in Mathematics Dept. | 28681 |
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| 515.45 LOV Linear integral Equations. | 515.45 POR Integral equations | 515.5 AND Special functions | 515.5 AND Special Functions | 515.5 LAB Special functions and their applications. | 515.55 DEI Orthogonal polynomials and random matrices | 515.55 DUN Orthogonal Polynomials of Several Variables |
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
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."--BOOK JACKET. "The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This 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."--Jacket
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