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11—20 of 36 matching pages
11: Bibliography T
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On the connection formula for the first Painlevé equation—from the viewpoint of the exact WKB analysis.
Sūrikaisekikenkyūsho Kōkyūroku (931), pp. 70–99.
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On exact solutions to the cylindrical Poisson-Boltzmann equation with applications to polyelectrolytes.
Phys. A 244 (1-4), pp. 402–413.
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12: Bibliography M
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Exact remainders for asymptotic expansions of fractional integrals.
J. Inst. Math. Appl. 24 (2), pp. 139–147.
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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. I. The equal-means case.
J. Multivariate Anal. 77 (1), pp. 21–53.
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Exact misclassification probabilities for plug-in normal quadratic discriminant functions. II. The heterogeneous case.
J. Multivariate Anal. 82 (2), pp. 299–330.
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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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13: 18.40 Methods of Computation
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14: Bibliography S
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Exact recursive evaluation of - and -coefficients for quantum-mechanical coupling of angular momenta.
J. Mathematical Phys. 16 (10), pp. 1961–1970.
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Exact analytical solutions of
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J. Math. Anal. Appl. 43 (3), pp. 626–632.
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Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels.
SIAM J. Math. Anal. 11 (5), pp. 828–841.
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Root-rational-fraction package for exact calculation of vector-coupling coefficients.
Comput. Phys. Comm. 21 (2), pp. 195–205.
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15: Bibliography I
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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16: 5.11 Asymptotic Expansions
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►Wrench (1968) gives exact values of up to .
Spira (1971) corrects errors in Wrench’s results and also supplies exact and 45D values of for .
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17: 18.38 Mathematical Applications
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►If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the th degree OP with the same weight function, and the interval of orthogonality is the same as the integration range, then the weights in the quadrature formula can be chosen in such a way that the formula is exact for all polynomials of degree not exceeding .
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►However, by using Hirota’s technique of bilinear formalism of soliton theory, Nakamura (1996) shows that a wide class of exact solutions of the Toda equation can be expressed in terms of various special functions, and in particular classical OP’s.
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18: 36.10 Differential Equations
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19: Bibliography P
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The exact distribution of the Wald statistic.
Econometrica 54 (4), pp. 881–895.
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20: Bibliography W
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Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region.
Phys. Rev. B 13, pp. 316–374.
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