Handbook of Mathematical Functions

Description

Title Errata Preface Preface to the Ninth Printing Foreword Contents Introduction 2. Physical Constants and Conversion Factors A. G. McNish 3. Elementary Analytical Methods M. Abramowitz 3.1. Binomial Theorem and Binomial Coefficients; Arithmetic and Geometric Progressions; Arithmetic, Geometric, Harmonic and Generalized Means 3.2. Inequalities 3.3. Rules for Differentiation and Integration 3.4. Limits, Maxima and Minima 3.5. Absolute and Relative Errors 3.6. Infinite Series 3.7. Complex Numbers and Functions 3.8. Algebraic Equations 3.9. Successive Approximation Methods 3.10. Theorems on Continued Fractions References 4. Elementary Transcendental Functions R. Zucker 4.1. Logarithmic Function 4.2. Exponential Function 4.3. Circular Functions 4.4. Inverse Circular Functions 4.5. Hyperbolic Functions 4.6. Inverse Hyperbolic Functions References 5. Exponential Integral and Related Functions W. Gautschi, W. F. Cahill 5.1. Exponential Integral 5.2. Sine and Cosine Integrals References 6. Gamma Function and Related Functions P. J. Davis 6.1. Gamma Function 6.2. Beta Function 6.3. Psi (Digamma) Function 6.4. Polygamma Functions 6.5. Incomplete Gamma Function 6.6. Incomplete Beta Function References 7. Error Function and Fresnel Integrals W. Gautschi 7.1. Error Function 7.2. Repeated Integrals of the Error Function 7.3. Fresnel Integrals 7.4. Definite and Indefinite Integrals References 8. Legendre Functions I. A. Stegun References 9. Bessel Functions of Integer Order F. W. J. Olver Bessel Functions J and Y Modified Bessel Functions I and K Kelvin Functions References 10. Bessel Functions of Fractional Order H. A. Antosiewicz 10.1. Spherical Bessel Functions 10.2. Modified Spherical Bessel Functions 10.3. Riccati-Bessel Functions 10.4. Airy Functions References 11. Integrals of Bessel Functions Y. L. Luke 11.1. Simple Integrals of Bessel Functions 11.2. Repeated Integrals of J and K 11.3. Reduction Formulas for Indefinite Integrals 11.4. Definite Integrals References 12. Struve Functions and Related Functions M. Abramowitz 12.1. Struve Function H 12.2. Modified Struve Function L 12.3. Anger and Weber Functions References 13. Confluent Hypergeometric Functions L. J. Slater References 14. Coulomb Wave Functions M. Abramowitz References 15. Hypergeometric Functions F. Oberhettinger References 16. Jacobian Elliptic Functions and Theta Functions L. M. Milne-Thomson Jacobian Elliptic Functions Theta Functions References 17. Elliptic Integrals L. M. Milne-Thomson 17.1. Definition of Elliptic Integrals 17.2. Canonical Forms 17.3. Complete Elliptic Integrals of the First and Second Kinds 17.4. Incomplete Elliptic Integrals of the First and Second Kinds 17.5. Landen's Transformation 17.6. The Process of the Arithmetic-Geometric Mean 17.7. Elliptic Integrals of the Third Kind References 18. Weierstrass Elliptic and Related Functions T. H. Southard References 19. Parabolic Cylinder Functions J. C. P. Miller The functions U and V The function W References 20. Mathieu Functions G. Blanch References 21. Spheroidal Wave Functions A. N. Lowan References 22. Orthogonal Polynomials U. W. Hochstrasser References 23. Bernoulli and Euler Polynomials, Riemann Zeta Function E. V. Haynsworth, K. Goldberg 23.1. Bernoulli and Euler Polynomials and the Euler-Maclaurin Formula 23.2. Riemann Zeta Function and Other Sums of Reciprocal Powers References 24. Combinatorial Analysis K. Goldberg, M. Newman, E. Haynsworth 24.1. Basic Numbers 24.2. Partitions 24.3. Number Theoretic Functions References 25. Numerical Interpolation, Differentiation and Integration P. J. Davis, I. Polonsky 25.1. Differences 25.2. Interpolation 25.3. Differentiation 25.4. Integration 25.5. Ordinary Differential Equations References 26. Probability Functions M. Zelen, N. C. Severo 26.1. Probability Functions: Definitions and Properties 26.2. Normal or Gaussian Probability Function 26.3. Bivariate Normal Probability Function 26.4. Chi-Square Probability Function 26.5. Incomplete Beta Function 26.6. F-(Variance-Ratio) Distribution Function 26.7. Student's t-Distribution References 27. Miscellaneous Functions I. A. Stegun 27.1. Debye Functions 27.2. Planck's Radiation Function 27.3. Einstein Functions 27.4. Sievert Integral 27.5. Unnamed and Related Integrals 27.6. Unnamed Integral 27.7. Dilogarithm (Spence's Integral) 27.8. Clausen's Integral and Related Summations 27.9. Vector-Addition Coefficients 29. Laplace Transforms References Subject Index Index of Notations