Mathematical Functions and Their Approximations

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