Arscott, F. M. 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). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 137 Documents Keywords:special functions PDFBibTeX XML 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 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