Nicholson-type%20integral
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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 absolutely integrable on for every finite , and the integral (1.14.47) converges, then … ►§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: 12.12 Integrals
§12.12 Integrals
… ►Nicholson-type Integral
… ►For further integrals see §§13.10, 13.23, and use (12.7.14). … ► ►See also Barr (1968) and Lowdon (1970).3: 8.19 Generalized Exponential Integral
§8.19 Generalized Exponential Integral
►§8.19(i) Definition and Integral Representations
… ►Other Integral Representations
… ►§8.19(ii) Graphics
… ►§8.19(x) Integrals
…4: 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
… ► …5: 8.21 Generalized Sine and Cosine Integrals
§8.21 Generalized Sine and Cosine Integrals
… ►§8.21(iii) Integral Representations
… ►§8.21(iv) Interrelations
… ►§8.21(v) Special Values
… ►6: 7.2 Definitions
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§7.2(ii) Dawson’s Integral
… ►§7.2(iii) Fresnel Integrals
… ►Values at Infinity
… ►§7.2(iv) Auxiliary Functions
… ►§7.2(v) Goodwin–Staton Integral
…7: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
.
Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
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Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results.
SIAM J. Math. Anal. 9 (1), pp. 76–86.
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8: 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
…9: 19.16 Definitions
…
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