Book:Milton Abramowitz/Handbook of mathematical functions

Milton Abramowitz and Irene A. Stegun: Mathematical Handbook of Formulas and Tables

Published $1964$, Dover Publications

ISBN 0-486-61272-4.

BiBTeX

@book {MR0167642,
    AUTHOR = {Abramowitz, Milton and Stegun, Irene A.},
     TITLE = {Handbook of mathematical functions with formulas, graphs, and
              mathematical tables},
    SERIES = {National Bureau of Standards Applied Mathematics Series},
    VOLUME = {55},
 PUBLISHER = {For sale by the Superintendent of Documents, U.S. Government
              Printing Office, Washington, D.C.},
      YEAR = {1964},
     PAGES = {xiv+1046},
   MRCLASS = {33.00 (65.05)},
  MRNUMBER = {0167642},
MRREVIEWER = {D. H. Lehmer},
}

Contents

Preface

Foreword

Introduction

1. Mathematical Constants

2. Physical Constants and Conversion Factors

3. Elementary Analytical Methods

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

3.11. Use and Extension of the Tables

3.12. Computing Techniques

4. Elementary Transcendental Functions: Logarithmic, Exponential, Circular and Hyperbolic Functions

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

4.7. Use and Extension of the Tables

5. Exponential Integral and Related Functions

5.1. Exponential Integral

5.2. Sine and Cosine Integrals

5.3. Use and Extension of the Tables

6. Gamma Function and Related Functions

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

6.7. Use and Extension of the Tables

6.8. Summation of Rational Series by Means of Polygamma Functions

7. Error Function and Fresnel Integrals

7.1. Error Function

7.2. Repeated Integrals of the Error Function

7.3. Fresnel Integrals

7.4. Definite and Indefinite Integrals

7.5. Use and Extension of the Tables

8. Legendre Functions

8.1. Differential Equation

8.2. Relations Between Legendre Functions

8.3. Values on the Cut

8.4. Explicit Expressions

8.5. Recurrence Relations

8.6. Special Values

8.7. Trigonometric Expressions

8.8. Integral Representations

8.9. Summation Formulas

8.10. Asymptotic Expansions

8.11. Toroidal Functions

8.12. Conical Functions

8.13. Relation to Elliptic Integrals

8.14. Integrals

8.15. Use and Extension of the Tables

9. Bessel Functions of Integer Order

9.1. Definitions and Elementary Properties

9.2. Asymptotic Expansions for Large Arguments

9.3. Asymptotic Expansions for Large Orders

9.4. Polynomial Approximations

9.5. Zeros

9.6. Definitions and Properties

9.7. Asymptotic Expansions

9.8. Polynomial Approximations

9.9. Definitions and Properties

9.10. Asymptotic Expansions

9.11. Polynomial Approximations

9.12. Use and Extension of the Tables

10. Bessel Functions of Fractional Order

10.1 Spherical Bessel Functions

10.2 Modified Spherical Bessel Functions

10.3 Riccati-Bessel Functions

10.4 Airy Functions

10.5 Use and Extension of the Tables

11. Integrals of Bessel Functions

11.1 Simple Integrals of Bessel Functions

11.2 Repeated Integrals of $J_n(z)$ and $K_0(z)$

11.3 Reduction Formulas for Indefinite Integrals

11.4 Definite Integrals

11.5 Use and Extensions of the Tables

12. Struve Functions and Related Functions

12.1 Struve Function $\mathbf{H}_{\nu}(z)$

12.2 Modified Struve Functions $\mathbf{L}_{\nu}(z)$

12.3 Anger and Weber Functions

12.4 Use and Extension of the Tables

13. Confluent Hypergeometric Functions

13.1 Definitions of Kummer and Whittaker Functions

13.2 Integral Representations

13.3 Connections With Bessel Functions

13.4 Recurrence Relations and Differential Properties

13.5 Asymptotic Expansions and Limiting Forms

13.6 Special Cases

13.7 Zeros and Turning Values

13.8 Use and Extension of the Tables

13.9 Calculation of the Zeros and Turning Points

13.10 Graphing $M(a,b,x)$

14. Coulomb Wave Functions

15. Hypergeometric Functions

16. Jacobian Elliptic Functions and Theta Functions

17. Elliptic Integrals

18. Weierstrass Elliptic and Related Functions

19. Parabolic Cylinder Functions

20. Mathieu Functions

21. Spheroidal Wave Functions

22. Orthogonal Polynomials

23. Bernoulli and Euler Polynomials, Riemann Zeta Function

24. Combinatorial Analysis

25. Numerical Interpolation, Differentiation and Integration

26. Probability Functions

27. Miscellaneous Functions

28. Scales of Notation

29. Laplace Transforms

Subject Index

Index of Notations