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Mathieusche Funktionen und Sphäroid-Funktionen mit Anwendungen auf physikalische und technische Probleme. (German) Zbl 0058.29503

(Die Grundlehren der mathematischen Wissenschaften. Bd. LXXI.) Berlin- Göttingen-Heidelberg: Springer-Verlag. 414 S. mit 29 Abb. (1954).

Digital Library of Mathematical Functions:

§28.10(i) Equations with Elementary Kernels ‣ §28.10 Integral Equations ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.11 Expansions in Series of Mathieu Functions ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.12(iii) Functions ce ν ( z , q ) , se ν ( z , q ) , when ∉ ν Z ‣ §28.12 Definitions and Basic Properties ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.12(ii) Eigenfunctions me ν ( z , q ) ‣ §28.12 Definitions and Basic Properties ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.12(i) Eigenvalues λ + ν ⁢ 2 n ( q ) ‣ §28.12 Definitions and Basic Properties ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.14 Fourier Series ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.15(ii) Solutions me ν ( z , q ) ‣ §28.15 Expansions for Small q ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.15(i) Eigenvalues λ ν ( q ) ‣ §28.15 Expansions for Small q ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.16 Asymptotic Expansions for Large q ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.17 Stability as → x ± ∞ ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.19 Expansions in Series of me + ν ⁢ 2 n Functions ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Table 28.1.1 ‣ §28.1 Special Notation ‣ Notation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.20(iii) Solutions M ( j ) ν ‣ §28.20 Definitions and Basic Properties ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.20(ii) Solutions Ce ν , Se ν , Me ν , Fe n , Ge n ‣ §28.20 Definitions and Basic Properties ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.20(vii) Shift of Variable ‣ §28.20 Definitions and Basic Properties ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.20(vi) Wronskians ‣ §28.20 Definitions and Basic Properties ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.22(ii) Noninteger ν ‣ §28.22 Connection Formulas ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.22(i) Integer ν ‣ §28.22 Connection Formulas ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.23 Expansions in Series of Bessel Functions ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.25 Asymptotic Expansions for Large ℜ z ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.28(i) Equations with Elementary Kernels ‣ §28.28 Integrals, Integral Representations, and Integral Equations ‣ Modified Mathieu Functions ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.2(iii) Floquet’s Theorem and the Characteristic Exponents ‣ §28.2 Definitions and Basic Properties ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.2(ii) Basic Solutions w I , w II ‣ §28.2 Definitions and Basic Properties ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.2(iv) Floquet Solutions ‣ §28.2 Definitions and Basic Properties ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.2(vi) Eigenfunctions ‣ §28.2 Definitions and Basic Properties ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.2(v) Eigenvalues a n , b n ‣ §28.2 Definitions and Basic Properties ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
2nd item ‣ §28.33(ii) Boundary-Value Problems ‣ §28.33 Physical Applications ‣ Applications ‣ Chapter 28 Mathieu Functions and Hill’s Equation
3rd item ‣ §28.33(iii) Stability and Initial-Value Problems ‣ §28.33 Physical Applications ‣ Applications ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.33(ii) Boundary-Value Problems ‣ §28.33 Physical Applications ‣ Applications ‣ Chapter 28 Mathieu Functions and Hill’s Equation
item (e) ‣ §28.34(ii) Eigenvalues ‣ §28.34 Methods of Computation ‣ Computation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
item (d) ‣ §28.34(iii) Floquet Solutions ‣ §28.34 Methods of Computation ‣ Computation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(iii) Normalization ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(ii) Recurrence Relations ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(i) Definitions ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(iv) Case = q 0 ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(vi) Behavior for Small q ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(v) Change of Sign of q ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.4(vi) Behavior for Small q ‣ §28.4 Fourier Series ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.5(i) Definitions ‣ §28.5 Second Solutions fe n , ge n ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Wronskians ‣ §28.5(i) Definitions ‣ §28.5 Second Solutions fe n , ge n ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.6(ii) Functions ce n and se n ‣ §28.6 Expansions for Small q ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.6(i) Eigenvalues ‣ §28.6 Expansions for Small q ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.7 Analytic Continuation of Eigenvalues ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.7 Analytic Continuation of Eigenvalues ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.8(i) Eigenvalues ‣ §28.8 Asymptotic Expansions for Large q ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.8(ii) Sips’ Expansions ‣ §28.8 Asymptotic Expansions for Large q ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.9 Zeros ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
§30.10 Series and Integrals ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(iii) Asymptotic Behavior ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(iii) Asymptotic Behavior ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(iv) Wronskian ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(vi) Integral Representations ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(v) Connection with the Ps and Qs Functions ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(vi) Integral Representations ‣ §30.11 Radial Spheroidal Wave Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.13(iii) Laplacian ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.13(ii) Metric Coefficients ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.13(i) Prolate Spheroidal Coordinates ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.13(iv) Separation of Variables ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.13(v) The Interior Dirichlet Problem for Prolate Ellipsoids ‣ §30.13 Wave Equation in Prolate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(iii) Laplacian ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(ii) Metric Coefficients ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(i) Oblate Spheroidal Coordinates ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(iv) Separation of Variables ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.14(v) The Interior Dirichlet Problem for Oblate Ellipsoids ‣ §30.14 Wave Equation in Oblate Spheroidal Coordinates ‣ Applications ‣ Chapter 30 Spheroidal Wave Functions
§30.16(i) Eigenvalues ‣ §30.16 Methods of Computation ‣ Computation ‣ Chapter 30 Spheroidal Wave Functions
§30.16(i) Eigenvalues ‣ §30.16 Methods of Computation ‣ Computation ‣ Chapter 30 Spheroidal Wave Functions
§30.1 Special Notation ‣ Notation ‣ Chapter 30 Spheroidal Wave Functions
§30.2(ii) Other Forms ‣ §30.2 Differential Equations ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.2(i) Spheroidal Differential Equation ‣ §30.2 Differential Equations ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.3(iii) Transcendental Equation ‣ §30.3 Eigenvalues ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.3(ii) Properties ‣ §30.3 Eigenvalues ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.3(i) Definition ‣ §30.3 Eigenvalues ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.3(iv) Power-Series Expansion ‣ §30.3 Eigenvalues ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.4(ii) Elementary Properties ‣ §30.4 Functions of the First Kind ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.4(i) Definitions ‣ §30.4 Functions of the First Kind ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.4(iv) Orthogonality ‣ §30.4 Functions of the First Kind ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.5 Functions of the Second Kind ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.5 Functions of the Second Kind ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.6 Functions of Complex Argument ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
Values on ( - 1 , 1 ) ‣ §30.6 Functions of Complex Argument ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.8(ii) Functions of the Second Kind ‣ §30.8 Expansions in Series of Ferrers Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.8(i) Functions of the First Kind ‣ §30.8 Expansions in Series of Ferrers Functions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.9(ii) Oblate Spheroidal Wave Functions ‣ §30.9 Asymptotic Approximations and Expansions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.9(i) Prolate Spheroidal Wave Functions ‣ §30.9 Asymptotic Approximations and Expansions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.9(ii) Oblate Spheroidal Wave Functions ‣ §30.9 Asymptotic Approximations and Expansions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.9(i) Prolate Spheroidal Wave Functions ‣ §30.9 Asymptotic Approximations and Expansions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
Chapter 30 Spheroidal Wave Functions
Notations P ‣ Notations
Notations P ‣ Notations
Notations Q ‣ Notations
Notations Q ‣ Notations