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21—30 of 31 matching pages
21: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Cyclic identities for Jacobi elliptic and related functions.
J. Math. Phys. 44 (4), pp. 1822–1841.
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Cyclic identities involving Jacobi elliptic functions.
J. Math. Phys. 43 (7), pp. 3798–3806.
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Connecting Jacobi elliptic functions with different modulus parameters.
Pramana 63 (5), pp. 921–936.
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22: Bibliography M
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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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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function.
Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
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Jacobian Elliptic Function Tables.
Dover Publications Inc., New York.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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23: Errata
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Equations (22.19.6), (22.19.7), (22.19.8),
(22.19.9)
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Equation (22.19.2)
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Table 22.4.3
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Chapters 8, 20, 36
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References
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These equations were rewritten with the modulus (second argument) of the Jacobian elliptic function defined explicitly in the preceding line of text.
22.19.2
Originally the first argument to the function was given incorrectly as . The correct argument is .
Reported 2014-03-05 by Svante Janson.
Originally a minus sign was missing in the entries for and in the second column (headed ). The correct entries are and . Note: These entries appear online but not in the published print edition. More specifically, Table 22.4.3 in the published print edition is restricted to the three Jacobian elliptic functions , whereas Table 22.4.3 covers all 12 Jacobian elliptic functions.
Reported 2014-02-28 by Svante Janson.
24: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Smithsonian Elliptic Functions Tables.
Smithsonian Miscellaneous Collections, v. 109 (Publication
3863), The Smithsonian Institution, Washington, D.C..
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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Numerical Methods Based on Sinc and Analytic Functions.
Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
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25: Bibliography W
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Evaluating elliptic functions and their inverses.
Comput. Math. Appl. 39 (3-4), pp. 131–136.
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Elliptic Functions. A Constructive Approach.
John Wiley & Sons Ltd., Chichester-New York.
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The distribution of the zeros of Jacobian elliptic functions with respect to the parameter
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Comput. Methods Funct. Theory 9 (2), pp. 579–591.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Elliptic Functions According to Eisenstein and Kronecker.
Classics in Mathematics, Springer-Verlag, Berlin.
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26: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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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
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Integral representations for elliptic functions.
J. Math. Anal. Appl. 316 (1), pp. 142–160.
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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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27: 36.5 Stokes Sets
28: Bibliography P
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Tables of Digamma and Trigamma Functions.
In Tracts for Computers, No. 1, K. Pearson (Ed.),
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Exponential asymptotics of the Mittag-Leffler function.
Proc. Roy. Soc. London Ser. A 458, pp. 3041–3052.
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Tables of the Incomplete Elliptic Integrals of the First and Third Kind.
Technical report
Curtiss-Wright Corp., Research Division, Quehanna, PA.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Elliptic integrals.
Computers in Physics 4 (1), pp. 92–96.
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29: 20.7 Identities
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§20.7(i) Sums of Squares
… ►§20.7(v) Watson’s Identities
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… ►§20.7(vii) Derivatives of Ratios of Theta Functions
… ►See Lawden (1989, pp. 19–20). …30: Bibliography O
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Complete elliptic integrals resulting from infinite integrals of Bessel functions.
J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.
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Complete elliptic integrals resulting from infinite integrals of Bessel functions. II.
J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.
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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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Whittaker functions with both parameters large: Uniform approximations in terms of parabolic cylinder functions.
Proc. Roy. Soc. Edinburgh Sect. A 86 (3-4), pp. 213–234.
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Distribution of the partition function modulo
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Ann. of Math. (2) 151 (1), pp. 293–307.
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