integral%20equation%20for%20Lam%C3%A9%20functions
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1: 1.14 Integral Transforms
§1.14 Integral Transforms
… ►where the last integral denotes the Cauchy principal value (1.4.25). … ►If is integrable on for all in , then the integral (1.14.32) converges and is an analytic function of in the vertical strip . … ►§1.14(viii) Compendia
►For more extensive tables of the integral transforms of this section and tables of other integral transforms, see Erdélyi et al. (1954a, b), Gradshteyn and Ryzhik (2000), Marichev (1983), Oberhettinger (1972, 1974, 1990), Oberhettinger and Badii (1973), Oberhettinger and Higgins (1961), Prudnikov et al. (1986a, b, 1990, 1992a, 1992b).2: 7.2 Definitions
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§7.2(ii) Dawson’s Integral
… ►§7.2(iii) Fresnel Integrals
… ► , , and are entire functions of , as are and in the next subsection. … ►§7.2(iv) Auxiliary Functions
… ►§7.2(v) Goodwin–Staton Integral
…3: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
►§8.19(i) Definition and Integral Representations
… ►Other Integral Representations
… ►§8.19(vi) Relation to Confluent Hypergeometric Function
… ►§8.19(x) Integrals
…4: 7.18 Repeated Integrals of the Complementary Error Function
§7.18 Repeated Integrals of the Complementary Error Function
►§7.18(i) Definition
… ►§7.18(iii) Properties
… ► … ►Hermite Polynomials
…5: 6.2 Definitions and Interrelations
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§6.2(i) Exponential and Logarithmic Integrals
… ►The logarithmic integral is defined by … ►§6.2(ii) Sine and Cosine Integrals
… ► is an odd entire function. … ►§6.2(iii) Auxiliary Functions
…6: 19.16 Definitions
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§19.16(i) Symmetric Integrals
… ►Just as the elementary function (§19.2(iv)) is the degenerate case … ►§19.16(ii)
►All elliptic integrals of the form (19.2.3) and many multiple integrals, including (19.23.6) and (19.23.6_5), are special cases of a multivariate hypergeometric function …The -function is often used to make a unified statement of a property of several elliptic integrals. …7: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
… ►§8.21(iii) Integral Representations
… ►Spherical-Bessel-Function Expansions
… ►§8.21(viii) Asymptotic Expansions
… ►8: 19.2 Definitions
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§19.2(i) General Elliptic Integrals
… ►§19.2(ii) Legendre’s Integrals
… ►The principal values of and are even functions. … ►§19.2(iii) Bulirsch’s Integrals
… ►§19.2(iv) A Related Function:
…9: 29.2 Differential Equations
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