×

Handbook of mathematical functions with formulas, graphs and mathematical tables. (English) Zbl 0171.38503

Washington: U.S. Department of Commerce. xiv, 1046 pp. (1964).
Dieses umfassende Werk über das Gebiet der speziellen Funktionen vereint eine Vielzahl von Tafeln und dazugehörigen Formeln. 29 Kapitel wurden von 28 Autoren bearbeitet. Die Tafeln sind teilweise von sehr hoher Genauigkeit, z. B. sind die trigonometrischen Funktionen mit 23 Stellen wiedergegeben. Im einzelnen sind in dem Buch Tafeln enthalten über mathematische und physikalische Konstanten, elementare transzendente Funktionen, Integralsinus und verwandte Funktionen, Gammafunktionen und Verwandte, Fehlerintegral und Fresnelsche Integrale, Legendresche Funktionen, Besselsche Funktionen und Integrale, Struvesche Funktionen und Verwandte, hypergeometrische und konfluente hypergeometrische Funktionen, elliptische Funktionen und Integrale, parabolische Zylinderfunktionen und eine Anzahl weiterer spezieller Funktionen.
Ein Kapitel unter der Überschrift ,, Elementare analytische Methoden” enthält eine nützliche Formelsammlung und Tafeln von Potenzen und Wurzeln. Ein weiteres Kapitel ist der numerischen Integration, Differentiation und Interpolation gewidmet und enthält ebenfalls eine Anzahl von Tafeln, etwa die Lagrangeschen Interpolationskoeffizienten bis achter Ordnung oder Abzissen und Gewichte der Gaußschen Quadraturformeln auf 20 Stellen. In weiteren Kapiteln werden Mathieusche Funktionen, Orthogonalpolynome, Bernoullische und Eulersche Polynome sowie die Riemannsche Zetafunktion, statistische Verteilungsfunktion und Laplace-Transformationen behandelt.
Ein umfangreiches Kapitel ist der Kombinatorik und zahlentheoretischen Funktionen gewidmet.
Mit diesem Buch dürfte das Standardtafelwerk vorliegen, das für viele Zwecke spezielle und umfangreiche Tafeln und Formelsammlungen erasetzen kann oder sogar übertrifft.
Table Errata, see Math. Comput. 21, 747 (1967).
Reviewer: K.-H. Bachmann

MSC:

33-00 General reference works (handbooks, dictionaries, bibliographies, etc.) pertaining to special functions
00A20 Dictionaries and other general reference works
00A22 Formularies
65A05 Tables in numerical analysis
65Dxx Numerical approximation and computational geometry (primarily algorithms)
41A55 Approximate quadratures
62Q05 Statistical tables
44A10 Laplace transform
11B68 Bernoulli and Euler numbers and polynomials
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11Y70 Values of arithmetic functions; tables

Digital Library of Mathematical Functions:

§10.1 Special Notation ‣ Notation ‣ Chapter 10 Bessel Functions
§10.21(ix) Complex Zeros ‣ §10.21 Zeros ‣ Bessel and Hankel Functions ‣ Chapter 10 Bessel Functions
§10.47(i) Differential Equations ‣ §10.47 Definitions and Basic Properties ‣ Spherical Bessel Functions ‣ Chapter 10 Bessel Functions
§10.68(iv) Further Properties ‣ §10.68 Modulus and Phase Functions ‣ Kelvin Functions ‣ Chapter 10 Bessel Functions
§10.70 Zeros ‣ Kelvin Functions ‣ Chapter 10 Bessel Functions
2nd item ‣ §10.75(xi) Kelvin Functions and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
4th item ‣ §10.75(ii) Bessel Functions and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
4th item ‣ Real Zeros ‣ §10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
5th item ‣ Real Zeros ‣ §10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
1st item ‣ Complex Zeros ‣ §10.75(iii) Zeros and Associated Values of the Bessel Functions, Hankel Functions, and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
1st item ‣ §10.75(iv) Integrals of Bessel Functions ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
4th item ‣ §10.75(v) Modified Bessel Functions and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
1st item ‣ §10.75(vii) Integrals of Modified Bessel Functions ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
1st item ‣ §10.75(ix) Spherical Bessel Functions, Modified Spherical Bessel Functions, and their Derivatives ‣ §10.75 Tables ‣ Computation ‣ Chapter 10 Bessel Functions
Chapter 10 Bessel Functions
§11.10(vi) Relations to Other Functions ‣ §11.10 Anger–Weber Functions ‣ Related Functions ‣ Chapter 11 Struve and Related Functions
1st item ‣ §11.14(ii) Struve Functions ‣ §11.14 Tables ‣ Computation ‣ Chapter 11 Struve and Related Functions
1st item ‣ §11.14(iii) Integrals ‣ §11.14 Tables ‣ Computation ‣ Chapter 11 Struve and Related Functions
Chapter 11 Struve and Related Functions
1st item ‣ §12.19 Tables ‣ Computation ‣ Chapter 12 Parabolic Cylinder Functions
Chapter 12 Parabolic Cylinder Functions
3rd item ‣ §13.30 Tables ‣ Computation ‣ Chapter 13 Confluent Hypergeometric Functions
Chapter 13 Confluent Hypergeometric Functions
1st item ‣ §14.33 Tables ‣ Computation ‣ Chapter 14 Legendre and Related Functions
Chapter 14 Legendre and Related Functions
Chapter 15 Hypergeometric Function
Hermite ‣ §18.14(i) Upper Bounds ‣ §18.14 Inequalities ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials
§18.3 Definitions ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials
§18.41(ii) Zeros ‣ §18.41 Tables ‣ Computation ‣ Chapter 18 Orthogonal Polynomials
§18.41(i) Polynomials ‣ §18.41 Tables ‣ Computation ‣ Chapter 18 Orthogonal Polynomials
Hermite ‣ §18.5(iv) Numerical Coefficients ‣ §18.5 Explicit Representations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials
§18.8 Differential Equations ‣ Classical Orthogonal Polynomials ‣ Chapter 18 Orthogonal Polynomials
§19.14(ii) General Case ‣ §19.14 Reduction of General Elliptic Integrals ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals
§19.14(i) Examples ‣ §19.14 Reduction of General Elliptic Integrals ‣ Legendre’s Integrals ‣ Chapter 19 Elliptic Integrals
§19.1 Special Notation ‣ Notation ‣ Chapter 19 Elliptic Integrals
§19.25(v) Jacobian Elliptic Functions ‣ §19.25 Relations to Other Functions ‣ Symmetric Integrals ‣ Chapter 19 Elliptic Integrals
§19.36(iii) Via Theta Functions ‣ §19.36 Methods of Computation ‣ Computation ‣ Chapter 19 Elliptic Integrals
Functions K ( k ) and E ( k ) ‣ §19.37(ii) Legendre’s Complete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
Functions K ( k ) and E ( k ) ‣ §19.37(ii) Legendre’s Complete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
Function exp ( - / ⁢ π K ′ ( k ) K ( k ) ) ( = q ( k ) ) ‣ §19.37(ii) Legendre’s Complete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
Function exp ( - / ⁢ π K ′ ( k ) K ( k ) ) ( = q ( k ) ) ‣ §19.37(ii) Legendre’s Complete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
Functions F ( ϕ , k ) and E ( ϕ , k ) ‣ §19.37(iii) Legendre’s Incomplete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
Function Π ( ϕ , α 2 , k ) ‣ §19.37(iii) Legendre’s Incomplete Integrals ‣ §19.37 Tables ‣ Computation ‣ Chapter 19 Elliptic Integrals
§19.38 Approximations ‣ Computation ‣ Chapter 19 Elliptic Integrals
Chapter 19 Elliptic Integrals
§20.15 Tables ‣ Computation ‣ Chapter 20 Theta Functions
Chapter 20 Theta Functions
§22.15(ii) Representations as Elliptic Integrals ‣ §22.15 Inverse Functions ‣ Properties ‣ Chapter 22 Jacobian Elliptic Functions
§22.1 Special Notation ‣ Notation ‣ Chapter 22 Jacobian Elliptic Functions
Chapter 22 Jacobian Elliptic Functions
Other Notations ‣ §23.1 Special Notation ‣ Notation ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
Rhombic Lattice ‣ §23.20(i) Conformal Mappings ‣ §23.20 Mathematical Applications ‣ Applications ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
§23.23 Tables ‣ Computation ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
§23.23 Tables ‣ Computation ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
§23.9 Laurent and Other Power Series ‣ Weierstrass Elliptic Functions ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
§23.9 Laurent and Other Power Series ‣ Weierstrass Elliptic Functions ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
§23.9 Laurent and Other Power Series ‣ Weierstrass Elliptic Functions ‣ Chapter 23 Weierstrass Elliptic and Modular Functions
Chapter 23 Weierstrass Elliptic and Modular Functions
§24.20 Tables ‣ Computation ‣ Chapter 24 Bernoulli and Euler Polynomials
§24.2(iv) Tables ‣ §24.2 Definitions and Generating Functions ‣ Properties ‣ Chapter 24 Bernoulli and Euler Polynomials
Chapter 24 Bernoulli and Euler Polynomials
1st item ‣ §25.19 Tables ‣ Computation ‣ Chapter 25 Zeta and Related Functions
Alternative Notations ‣ §26.1 Special Notation ‣ Notation ‣ Chapter 26 Combinatorial Analysis
Alternative Notations ‣ §26.1 Special Notation ‣ Notation ‣ Chapter 26 Combinatorial Analysis
§26.21 Tables ‣ Computation ‣ Chapter 26 Combinatorial Analysis
§26.2 Basic Definitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.3(i) Definitions ‣ §26.3 Lattice Paths: Binomial Coefficients ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.4(i) Definitions ‣ §26.4 Lattice Paths: Multinomial Coefficients and Set Partitions ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§26.8(i) Definitions ‣ §26.8 Set Partitions: Stirling Numbers ‣ Properties ‣ Chapter 26 Combinatorial Analysis
§27.21 Tables ‣ Computation ‣ Chapter 27 Functions of Number Theory
§27.2(ii) Tables ‣ §27.2 Functions ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory
Abramowitz and Stegun (1964, Chapter 20) ‣ §28.1 Special Notation ‣ Notation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
Other Notations ‣ §30.1 Special Notation ‣ Notation ‣ Chapter 30 Spheroidal Wave Functions
Chapter 30 Spheroidal Wave Functions
1st item ‣ §33.24 Tables ‣ Computation ‣ Chapter 33 Coulomb Functions
Chapter 33 Coulomb Functions
§4.44 Other Applications ‣ Applications ‣ Chapter 4 Elementary Functions
§4.46 Tables ‣ Computation ‣ Chapter 4 Elementary Functions
Terminology ‣ §5.11(i) Poincaré-Type Expansions ‣ §5.11 Asymptotic Expansions ‣ Properties ‣ Chapter 5 Gamma Function
§5.22(iii) Complex Variables ‣ §5.22 Tables ‣ Computation ‣ Chapter 5 Gamma Function
§5.22(ii) Real Variables ‣ §5.22 Tables ‣ Computation ‣ Chapter 5 Gamma Function
§5.7(i) Maclaurin and Taylor Series ‣ §5.7 Series Expansions ‣ Properties ‣ Chapter 5 Gamma Function
Chapter 5 Gamma Function
1st item ‣ §6.19(ii) Real Variables ‣ §6.19 Tables ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
1st item ‣ §6.19(iii) Complex Variables, = z + x ⁢ i y ‣ §6.19 Tables ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
1st item ‣ §6.20(i) Approximations in Terms of Elementary Functions ‣ §6.20 Approximations ‣ Computation ‣ Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
Chapter 6 Exponential, Logarithmic, Sine, and Cosine Integrals
1st item ‣ §7.23(ii) Real Variables ‣ §7.23 Tables ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
2nd item ‣ §7.23(ii) Real Variables ‣ §7.23 Tables ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
1st item ‣ §7.23(iii) Complex Variables, = z + x ⁢ i y ‣ §7.23 Tables ‣ Computation ‣ Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
Chapter 7 Error Functions, Dawson’s and Fresnel Integrals
(8.17.24) ‣ §8.17(vii) Addendum to 8.17(i) Definitions and Basic Properties ‣ §8.17 Incomplete Beta Functions ‣ Related Functions ‣ Chapter 8 Incomplete Gamma and Related Functions
§8.22(ii) Riemann Zeta Function and Incomplete Riemann Zeta Function ‣ §8.22 Mathematical Applications ‣ Applications ‣ Chapter 8 Incomplete Gamma and Related Functions
1st item ‣ §8.26(iv) Generalized Exponential Integral ‣ §8.26 Tables ‣ Computation ‣ Chapter 8 Incomplete Gamma and Related Functions
Chapter 8 Incomplete Gamma and Related Functions
1st item ‣ §9.18(ii) Real Variables ‣ §9.18 Tables ‣ Computation ‣ Chapter 9 Airy and Related Functions
1st item ‣ §9.18(iv) Zeros ‣ §9.18 Tables ‣ Computation ‣ Chapter 9 Airy and Related Functions
1st item ‣ §9.18(v) Integrals ‣ §9.18 Tables ‣ Computation ‣ Chapter 9 Airy and Related Functions
§9.8(i) Definitions ‣ §9.8 Modulus and Phase ‣ Airy Functions ‣ Chapter 9 Airy and Related Functions
Chapter 9 Airy and Related Functions
Profile Frank W. J. Olver ‣ About the Project
About the Project
Preface ‣ About the Project
Possible Errors in DLMF ‣ Need Help?
Notations E ‣ Notations
Notations E ‣ Notations
Notations F ‣ Notations
Notations F ‣ Notations
Notations H ‣ Notations
Notations H ‣ Notations
Notations J ‣ Notations
Notations K ‣ Notations
Notations P ‣ Notations
Notations P ‣ Notations
Notations S ‣ Notations
Notations Y ‣ Notations