of type 2
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11—20 of 97 matching pages
11: Bibliography S
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Bounds for ratios of modified Bessel functions and associated Turán-type inequalities.
J. Math. Anal. Appl. 374 (2), pp. 516–528.
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On inequalities of the Turán type.
Math. Scand. 2, pp. 65–73.
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12: 19.2 Definitions
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19.2.6
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13: Bibliography P
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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14: 8.10 Inequalities
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►For further inequalities of these types see Qi and Mei (1999) and Neuman (2013).
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►For ,
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15: 12.12 Integrals
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12.12.3
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Nicholson-type Integral
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12.12.4
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►When
is real the left-hand side equals ; compare (12.2.22).
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►For compendia of integrals see Erdélyi et al. (1953b, v. 2, pp. 121–122), Erdélyi et al. (1954a, b, v. 1, pp. 60–61, 115, 210–211, and 336;
v. 2, pp. 76–80, 115, 151, 171, and 395–398), Gradshteyn and Ryzhik (2000, §7.7), Magnus et al. (1966, pp. 330–331), Marichev (1983, pp. 190–191), Oberhettinger (1974, pp. 144–145), Oberhettinger (1990, pp. 106–108 and 192), Oberhettinger and Badii (1973, pp. 181–185), Prudnikov et al. (1986b, pp. 36–37, 155–168, 243–246, 289–290, 327–328, 419–420, and 619), Prudnikov et al. (1992a, §3.11), and Prudnikov et al. (1992b, §3.11).
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16: 10.32 Integral Representations
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10.32.2
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10.32.8
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Mellin–Barnes Type
… ►In (10.32.14) the integration contour separates the poles of from the poles of . … ►Mellin–Barnes Type
…17: Bibliography T
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Numerical algorithms for uniform Airy-type asymptotic expansions.
Numer. Algorithms 15 (2), pp. 207–225.
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18: 7.7 Integral Representations
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►Integrals of the type
, where is an arbitrary rational function, can be written in closed form in terms of the error functions and elementary functions.
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19: 13.16 Integral Representations
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►In this subsection see §§10.2(ii), 10.25(ii) for the functions , , and , and §§15.1, 15.2(i) for .
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§13.16(iii) Mellin–Barnes Integrals
►If , then … ►If , then …where the contour of integration passes all the poles of on the right-hand side.20: 10.9 Integral Representations
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►Also, is continuous on the path, and takes its principal value at the intersection with the interval .
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