Mathematical Functions and Their Approximations

1st Edition - September 28, 1975
Author: Yudell L. Luke
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 2 - 6 2 4 5 - 1

Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at… Read more

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Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

PrefaceI. The Gamma Function and Related Functions 1.1 Definitions and Elementary Properties 1.2 Power Series and Other Series Expansions 1.3 Asymptotic Expansions 1.4 Rational Approximations for Ѱ (z) 1.5 Inequalities 1.6 Bibliographic and Numerical Data 1.6.1 General References 1.6.2 Description of and References to Tables 1.6.3 Description of and References to Other Approximations and ExpansionsII. The Binomial Function 2.1 Power Series 2.2 Expansions in Series of Jacobi and Chebyshev Polynomials 2.3 Expansions in Series of Bessel Functions 2.4 Padé Approximations 2.4.1 (1 + 1/z)-c 2.4.2 The Square Root 2.4.3 Padé Coefficients 2.4.4 The Function e-w 2.5 InequalitiesIII. Elementary Functions 3.1 Logarithmic Functions 3.1.1 Power Series 3.1.2 Expansion in Series of Chebyshev Polynomials 3.1.3 Padé Approximations 3.1.4 Inequalities 3.2 Exponential Function 3.2.1 Series Expansions 3.2.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions 3.2.3 Padé Approximations 3.2.4 Inequalities 3.3 Circular and Hyperbolic Functions 3.3.1 Power Series 3.3.2 Expansions in Series of Jacobi and Chebyshev Polynomials and Bessel Functions 3.3.3 Rational and Padé Approximations 3.3.4 Inequalities 3.4 Inverse Circular and Hyperbolic Functions 3.4.1 Power Series 3.4.2 Expansions in Series of Chebyshev Polynomials 3.4.3 Padé Approximations 3.4.4 Inequalities 3.5 Bibliographic and Numerical Data 3.5.1 Description of and References to Tables 3.5.2 Description of and References to Other Approximations and ExpansionsIV. Incomplete Gamma Functions 4.1 Definitions and Series Expansions 4.2 Differential Equations and Difference Equations 4.3 Padé Approximations 4.3.1 1F1 (1; v + 1;-z) 4.3.2 z1-vezГ(v,z) 4.3.3 The Error Tn(v,z) for