exact

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11—20 of 36 matching pages

11: Bibliography T

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Y. Takei (1995) 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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Notes:: Painlevé functions and asymptotic analysis (Japanese) (Kyoto, 1995)
External Links:: FullText, MathReview (Andrei A. Kapaev)
Referenced by:: §32.12(i).
Encodings:: BibTeX

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C. A. Tracy and H. Widom (1997) 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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External Links:: ISSN 0378-4371, Document, MathReview (Vitor R. Vieira)
Referenced by:: §32.11(iv).
Encodings:: BibTeX

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12: Bibliography M

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J. P. McClure and R. Wong (1979) Exact remainders for asymptotic expansions of fractional integrals. J. Inst. Math. Appl. 24 (2), pp. 139–147.

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External Links:: ISSN 0020-2932, Document, MathReview, ZentralBlatt
Referenced by:: §2.6(iii).
Encodings:: BibTeX

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H. R. McFarland and D. St. P. Richards (2001) 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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External Links:: ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

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H. R. McFarland and D. St. P. Richards (2002) 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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External Links:: ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

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S. C. Milne (2002) 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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External Links:: Document, ZentralBlatt
Referenced by:: §27.13(iv).
Encodings:: BibTeX

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S. C. Milne (1996) 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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External Links:: ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt
Referenced by:: §27.13(iv).
Encodings:: BibTeX

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13: 18.40 Methods of Computation

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See accompanying text — Figure 18.40.1: Histogram approximations to the Repulsive Coulomb–Pollaczek, RCP, weight function integrated over $[-1,x)$ , see Figure 18.39.2 for an exact result, for $Z=+1$ , shown for $N=12$ and $N=120$ . Magnify

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14: Bibliography S

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K. Schulten and R. G. Gordon (1975a) Exact recursive evaluation of

3j

- and

6j

-coefficients for quantum-mechanical coupling of angular momenta. J. Mathematical Phys. 16 (10), pp. 1961–1970.

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External Links:: Document, MathReview (J.-L. Calais)
Referenced by:: §34.13, §34.3(iii).
Encodings:: BibTeX

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C. E. Siewert and E. E. Burniston (1973) Exact analytical solutions of

ze^{z}=a

. J. Math. Anal. Appl. 43 (3), pp. 626–632.

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External Links:: Document, MathReview (Pl. Kannappan), ZentralBlatt
Referenced by:: §4.13.
Encodings:: BibTeX

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K. Soni (1980) 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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External Links:: ISSN 0036-1410, Document, MathReview (John S. Lew), ZentralBlatt
Referenced by:: §2.5(ii).
Encodings:: BibTeX

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A. J. Stone and C. P. Wood (1980) Root-rational-fraction package for exact calculation of vector-coupling coefficients. Comput. Phys. Comm. 21 (2), pp. 195–205.

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Notes:: Double-precision Fortran, maximum accuracy 16D
External Links:: Document, Code
Referenced by:: 10th item.
Encodings:: BibTeX

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15: Bibliography I

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Inverse Symbolic Calculator (website) Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.

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Notes:: From a decimal approximation, find the most likely exact value.
External Links:: Inverse Symbolic Calculator
Referenced by:: 3rd item.
Encodings:: BibTeX

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16: 5.11 Asymptotic Expansions

… ►Wrench (1968) gives exact values of

g_{k}

up to

g_{20}

. Spira (1971) corrects errors in Wrench’s results and also supplies exact and 45D values of

g_{k}

for

k=21,22,\dots,30

. …

17: 18.38 Mathematical Applications

… ►If the nodes in a quadrature formula with a positive weight function are chosen to be the zeros of the

n

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

2n-1

. … ►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. …

18: 36.10 Differential Equations

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19: Bibliography P

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P. C. B. Phillips (1986) The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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External Links:: ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

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20: Bibliography W

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T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch (1976) 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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External Links:: Document, Link
Referenced by:: §32.16, §32.16.
Encodings:: BibTeX

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