general%20values
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11—17 of 17 matching pages
11: Bibliography F
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Generalized parabolic cylinder functions.
Asymptotic Anal. 5 (6), pp. 517–531.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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12: 20.7 Identities
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►See Lawden (1989, pp. 19–20).
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►In the following equations , and all square roots assume their principal values.
…These are specific examples of modular transformations as discussed in §23.15; the corresponding results for the general case are given by Rademacher (1973, pp. 181–183).
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20.7.34
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13: 18.5 Explicit Representations
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18.5.5
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§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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Orthogonality of certain functions with respect to complex valued weights.
Canad. J. Math. 33 (5), pp. 1261–1270.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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15: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions
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►and in general,
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►Table 26.4.1 gives numerical values of multinomials and partitions for .
…For each all possible values of are covered.
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16: Bibliography O
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Tables of Lebedev, Mehler and Generalized Mehler Transforms.
Mathematical Note
Technical Report 246, Boeing Scientific Research Lab, Seattle.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Bessel Functions. Part III: Zeros and Associated Values.
Royal Society Mathematical Tables, Volume 7, Cambridge University Press, Cambridge-New York.
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General connection formulae for Liouville-Green approximations in the complex plane.
Philos. Trans. Roy. Soc. London Ser. A 289, pp. 501–548.
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Uniform, exponentially improved, asymptotic expansions for the generalized exponential integral.
SIAM J. Math. Anal. 22 (5), pp. 1460–1474.
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17: 18.40 Methods of Computation
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►For applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev.
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►There are many ways to implement these first two steps, noting that the expressions for and of equation (18.2.30) are of little practical numerical value, see Gautschi (2004) and Golub and Meurant (2010).
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18.40.6
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►Results of low ( to decimal digits) precision for are easily obtained for to .
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