double argument
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21—26 of 26 matching pages
21: Bibliography M
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The dilogarithm function for complex argument.
Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Derivatives of the Hurwitz zeta function for rational arguments.
J. Comput. Appl. Math. 100 (2), pp. 201–206.
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The dilogarithm function of a real argument.
Math. Comp. 33 (146), pp. 778–787.
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Further improvements of some double inequalities for bounding the gamma function.
Math. Comput. Modelling 57 (5-6), pp. 1360–1363.
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22: 25.6 Integer Arguments
23: Bibliography H
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Integrals that contain a probability function of complicated arguments.
Bul. Akad. Štiince RSS Moldoven. 1976 (1), pp. 80–84, 96 (Russian).
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Bessel functions of matrix argument.
Ann. of Math. (2) 61 (3), pp. 474–523.
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Algorithm AS66: The normal integral.
Appl. Statist. 22 (3), pp. 424–427.
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Two-center Coulomb functions.
Comput. Phys. Comm. 103 (2-3), pp. 209–216.
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24: 3.5 Quadrature
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►A second example is provided in Gil et al. (2001), where the method of contour integration is used to evaluate Scorer functions of complex argument (§9.12).
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3.5.47
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3.5.48
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25: 2.11 Remainder Terms; Stokes Phenomenon
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►However, on combining (2.11.6) with the connection formula (8.19.18), with , we derive
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►For large , with (), the Whittaker function of the second kind has the asymptotic expansion (§13.19)
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►For example, using double precision is found to agree with (2.11.31) to 13D.
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26: 34.4 Definition: Symbol
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►The symbol is defined by the following double sum of products of symbols:
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►where the summation is over all nonnegative integers such that the arguments in the factorials are nonnegative.
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►For alternative expressions for the symbol, written either as a finite sum or as other terminating generalized hypergeometric series of unit argument, see Varshalovich et al. (1988, §§9.2.1, 9.2.3).