integral representation
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11: 6.7 Integral Representations
§6.7 Integral Representations
… ► ►§6.7(ii) Sine and Cosine Integrals
… ►§6.7(iii) Auxiliary Functions
… ►For collections of integral representations see Bierens de Haan (1939, pp. 56–59, 72–73, 82–84, 121, 133–136, 155, 179–181, 223, 225–227, 230, 259–260, 374, 377, 397–398, 408, 416, 424, 431, 438–439, 442–444, 488, 496–500, 567–571, 585, 602, 638, 675–677), Corrington (1961), Erdélyi et al. (1954a, vol. 1, pp. 267–270), Geller and Ng (1969), Nielsen (1906b), Oberhettinger (1974, pp. 244–246), Oberhettinger and Badii (1973, pp. 364–371), and Watrasiewicz (1967).12: 7.7 Integral Representations
§7.7 Integral Representations
►§7.7(i) Error Functions and Dawson’s Integral
… ►§7.7(ii) Auxiliary Functions
… ►Mellin–Barnes Integrals
… ►For other integral representations see Erdélyi et al. (1954a, vol. 1, pp. 265–267, 270), Ng and Geller (1969), Oberhettinger (1974, pp. 246–248), and Oberhettinger and Badii (1973, pp. 371–377).13: 35.10 Methods of Computation
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►Other methods include numerical quadrature applied to double and multiple integral representations.
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14: 14.26 Uniform Asymptotic Expansions
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►See also Frenzen (1990), Gil et al. (2000), Shivakumar and Wong (1988), Ursell (1984), and Wong (1989) for uniform asymptotic approximations obtained from integral representations.
15: 5.14 Multidimensional Integrals
16: 9.17 Methods of Computation
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§9.17(iii) Integral Representations
►Among the integral representations of the Airy functions the Stieltjes transform (9.10.18) furnishes a way of computing in the complex plane, once values of this function can be generated on the positive real axis. …17: 1.17 Integral and Series Representations of the Dirac Delta
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§1.17(ii) Integral Representations
… ►Then comparison of (1.17.2) and (1.17.9) yields the formal integral representation … ►Sine and Cosine Functions
… ►Coulomb Functions (§33.14(iv))
… ►Airy Functions (§9.2)
…18: 14.32 Methods of Computation
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