Erdélyi, Arthur; Magnus, W.; Oberhettinger, F.; Tricomi, Francesco G. [Bateman, Harry] Higher transcendental functions. Vol. III. (English) Zbl 0064.06302 Bateman Manuscript Project, California Institute of Technology. New York: McGraw-Hill Book Co., XVII, 292 p. (1955). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 6 ReviewsCited in 624 Documents Keywords:special functions PDFBibTeX XML Digital Library of Mathematical Functions: §10.46 Generalized and Incomplete Bessel Functions; Mittag-Leffler Function ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions §27.2(i) Definitions ‣ §27.2 Functions ‣ Multiplicative Number Theory ‣ Chapter 27 Functions of Number Theory Chapter 27 Functions of Number Theory §28.10(iii) Further Equations ‣ §28.10 Integral Equations ‣ Mathieu Functions of Integer 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 §28.2(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(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 §29.10 Lamé Functions with Imaginary Periods ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.11 Lamé Wave Equation ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.14 Orthogonality ‣ Lamé Polynomials ‣ Chapter 29 Lamé Functions §29.17(iii) Lamé–Wangerin Functions ‣ §29.17 Other Solutions ‣ 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 §29.18(ii) Ellipsoidal Coordinates ‣ §29.18 Mathematical Applications ‣ Applications ‣ Chapter 29 Lamé Functions §29.18(iii) Spherical and Ellipsoidal Harmonics ‣ §29.18 Mathematical Applications ‣ Applications ‣ Chapter 29 Lamé Functions §29.18(i) Sphero-Conal Coordinates ‣ §29.18 Mathematical Applications ‣ Applications ‣ Chapter 29 Lamé Functions §29.1 Special Notation ‣ Notation ‣ Chapter 29 Lamé Functions §29.2(ii) Other Forms ‣ §29.2 Differential Equations ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.2(i) Lamé’s Equation ‣ §29.2 Differential Equations ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.3(ii) Distribution ‣ §29.3 Definitions and Basic Properties ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.3(i) Eigenvalues ‣ §29.3 Definitions and Basic Properties ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.3(ii) Distribution ‣ §29.3 Definitions and Basic Properties ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.3(iv) Lamé Functions ‣ §29.3 Definitions and Basic Properties ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.5 Special Cases and Limiting Forms ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.6(iii) Function 𝐸𝑠^{2𝑚+1}_𝜈(𝑧,𝑘²) ‣ §29.6 Fourier Series ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.6(ii) Function 𝐸𝑐^{2𝑚+1}_𝜈(𝑧,𝑘²) ‣ §29.6 Fourier Series ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.6(i) Function 𝐸𝑐^{2𝑚}_𝜈(𝑧,𝑘²) ‣ §29.6 Fourier Series ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.6(iv) Function 𝐸𝑠^{2𝑚+2}_𝜈(𝑧,𝑘²) ‣ §29.6 Fourier Series ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.8 Integral Equations ‣ Lamé Functions ‣ Chapter 29 Lamé Functions §29.8 Integral Equations ‣ Lamé Functions ‣ Chapter 29 Lamé Functions Chapter 29 Lamé Functions §30.10 Series and Integrals ‣ 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(i) Prolate Spheroidal Coordinates ‣ §30.13 Wave Equation in Prolate 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 §30.1 Special Notation ‣ Notation ‣ Chapter 30 Spheroidal Wave Functions §30.9(iii) Other Approximations and Expansions ‣ §30.9 Asymptotic Approximations and Expansions ‣ Properties ‣ Chapter 30 Spheroidal Wave Functions Chapter 30 Spheroidal Wave Functions §31.2(i) Heun’s Equation ‣ §31.2 Differential Equations ‣ Properties ‣ Chapter 31 Heun 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 Chapter 31 Heun Functions