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Periodic differential equations. An introduction to Mathieu, Lame, and allied functions. (English) Zbl 0121.29903

Int. Series of Monographs in Pure and Applied Mathematics. Vol. 66. Oxf.- Lond.-N.Y.-Paris: Pergamon Press 1964. X, 281 p. (1964).

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(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
§28.17 Stability as → x ± ∞ ‣ Mathieu Functions of Noninteger Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Arscott (1964b) and McLachlan (1947) ‣ §28.1 Special Notation ‣ Notation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Arscott (1964b) and McLachlan (1947) ‣ §28.1 Special Notation ‣ Notation ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.28(ii) Integrals of Products with Bessel Functions ‣ §28.28 Integrals, Integral Representations, and Integral Equations ‣ 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
§28.29(i) Hill’s Equation ‣ §28.29 Definitions and Basic Properties ‣ Hill’s Equation ‣ 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
§28.32(ii) Paraboloidal Coordinates ‣ §28.32 Mathematical Applications ‣ Applications ‣ Chapter 28 Mathieu Functions and Hill’s Equation
§28.32(i) Elliptical Coordinates and an Integral Relationship ‣ §28.32 Mathematical Applications ‣ Applications ‣ 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
§28.5(i) Definitions ‣ §28.5 Second Solutions fe n , ge n ‣ Mathieu Functions of Integer Order ‣ Chapter 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
§29.11 Lamé Wave Equation ‣ Lamé Functions ‣ Chapter 29 Lamé Functions
§29.12(iii) Zeros ‣ §29.12 Definitions ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.12(ii) Algebraic Form ‣ §29.12 Definitions ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.12(i) Elliptic-Function Form ‣ §29.12 Definitions ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.14 Orthogonality ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.15(ii) Chebyshev Series ‣ §29.15 Fourier Series and Chebyshev Series ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.15(ii) Chebyshev Series ‣ §29.15 Fourier Series and Chebyshev Series ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.17(i) Second Solution ‣ §29.17 Other Solutions ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions
§29.18(iii) Spherical and Ellipsoidal Harmonics ‣ §29.18 Mathematical Applications ‣ Applications ‣ Chapter 29 Lamé Functions
§29.1 Special Notation ‣ Notation ‣ Chapter 29 Lamé Functions
Chapter 29 Lamé Functions
§30.10 Series and Integrals ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.11(i) Definitions ‣ §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
§30.1 Special Notation ‣ Notation ‣ Chapter 30 Spheroidal Wave Functions
§30.2(ii) Other Forms ‣ §30.2 Differential Equations ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions
§30.4(iii) Power-Series Expansion ‣ §30.4 Functions of the First Kind ‣ 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
Chapter 30 Spheroidal Wave Functions
§31.4 Solutions Analytic at Two Singularities: Heun Functions ‣ Properties ‣ Chapter 31 Heun Functions
§31.5 Solutions Analytic at Three Singularities: Heun Polynomials ‣ Properties ‣ Chapter 31 Heun Functions
§31.9(ii) Double Orthogonality ‣ §31.9 Orthogonality ‣ Properties ‣ Chapter 31 Heun Functions
Notations F ‣ Notations
Notations G ‣ Notations
Notations M ‣ Notations
Notations N ‣ Notations