Difference between revisions of "Book:Milton Abramowitz/Handbook of mathematical functions"

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(Created page with "{{Book|Mathematical Handbook of Formulas and Tables|1964|Dover Publications|0-486-61272-4|Milton Abramowitz|author2 = Irene A. Stegun}} ===BiBTeX=== <pre>@book {MR0167642,...")
 
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:2. Physical Constants and Conversion Factors
 
:2. Physical Constants and Conversion Factors
 
:3. Elementary Analytical Methods
 
:3. Elementary Analytical Methods
−
:4. Elementary Transcendental Functions
+
::3.1. Binomial Theorem and Binomial Coefficients; Arithmetic and Geometric Progressions; Arithmetic, Geometric, Harmonic and Generalized Means
−
:: Logarithmic, Exponential, Circular and Hyperbolic Functions
+
::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. 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. 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. 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. 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. 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. 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. 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. 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. 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
 
:14. Coulomb Wave Functions
 
:15. Hypergeometric Functions
 
:15. Hypergeometric Functions

Revision as of 01:42, 4 June 2016

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
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