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1: 3.1 Arithmetics and Error Measures

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§3.1(iii) Rational Arithmetics

►Computer algebra systems use exact rational arithmetic with rational numbers $p/q$, where $p$ and $q$ are multi-length integers. …

2: Bibliography S

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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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Double-precision Fortran, maximum accuracy 16D

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10th item.

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3: 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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ISSN 0020-2932, Document, MathReview, ZentralBlatt

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§2.6(iii).

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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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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

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§35.9.

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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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ISSN 0047-259X, Document, MathReview (Peter A. Lachenbruch), ZentralBlatt

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§35.9.

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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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Document, ZentralBlatt

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§27.13(iv).

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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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ISSN 0027-8424, MathReview (Ken Ono), ZentralBlatt

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§27.13(iv).

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4: Bibliography C

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Nonclassical Symmetry Reductions and Exact Solutions for Physically Significant Nonlinear Evolution Equations. In Nonlinear and Chaotic Phenomena in Plasmas, Solids and Fluids (Edmonton, AB, 1990), W. Rozmus and J. A. Tuszynski (Eds.), pp. 72–79.

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MathReview

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§29.19(ii).

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Special polynomials associated with rational solutions of the fifth Painlevé equation. J. Comput. Appl. Math. 178 (1-2), pp. 111–129.

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ISSN 0377-0427, Document, MathReview (Davide Batic), ZentralBlatt

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§32.8(v), §32.9(ii).

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Rational Chebyshev approximations for the exponential integral $E_1(x)$ . Math. Comp. 22 (103), pp. 641–649.

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FullText, MathReview, ZentralBlatt

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2nd item.

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Rational Chebyshev approximations for the error function. Math. Comp. 23 (107), pp. 631–637.

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2nd item.

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Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

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ISSN 1076-2787, Document, MathReview

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§19.6(i).

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5: 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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Painlevé functions and asymptotic analysis (Japanese) (Kyoto, 1995)

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FullText, MathReview (Andrei A. Kapaev)

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§32.12(i).

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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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ISSN 0378-4371, Document, MathReview (Vitor R. Vieira)

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§32.11(iv).

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Rational Chebyshev approximation for the Fermi-Dirac integral $F_{-3/2}(x)$ . Solid–State Electronics 41 (5), pp. 771–773.

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Document

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§25.21(vii).

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6: Bibliography B

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Integral equations and exact solutions for the fourth Painlevé equation. Proc. Roy. Soc. London Ser. A 437, pp. 1–24.

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ISSN 0962-8444, FullText, MathReview (Mehmet Can), ZentralBlatt

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§32.11(v), §32.2(iii).

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Application of uniform asymptotics to the second Painlevé transcendent. Arch. Rational Mech. Anal. 143 (3), pp. 241–271.

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ISSN 0945-8396, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

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§32.11(ii).

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Rational Chebyshev approximations for the inverse of the error function. Math. Comp. 30 (136), pp. 827–830.

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FullText, MathReview, ZentralBlatt

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§7.17(iii), §7.17(iii).

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Rational Chebyshev approximations for the Bickley functions $K{i}_n(x)$ . Math. Comp. 32 (143), pp. 876–886.

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ISSN 0025-5718, FullText, MathReview (H. Hochstadt), ZentralBlatt

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§10.76(iii).

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Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind. IMA J. Numer. Anal. 12 (4), pp. 519–526.

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ISSN 0272-4979, MathReview, ZentralBlatt

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§5.21, §5.24(ii).

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7: Bibliography I

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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.

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From a decimal approximation, find the most likely exact value.

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Inverse Symbolic Calculator

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3rd item.

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$q$-Hermite polynomials, biorthogonal rational functions, and $q$-beta integrals. Trans. Amer. Math. Soc. 346 (1), pp. 63–116.

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ISSN 0002-9947, FullText, MathReview (R. A. Askey), ZentralBlatt

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§18.28(vii).

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8: Bibliography K

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Determinant structure of the rational solutions for the Painlevé II equation. J. Math. Phys. 37 (9), pp. 4693–4704.

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ISSN 0022-2488, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

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§32.8(ii).

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Determinant structure of the rational solutions for the Painlevé IV equation. J. Phys. A 31 (10), pp. 2431–2446.

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ISSN 0305-4470, Document, MathReview (Andrei A. Kapaev), ZentralBlatt

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§32.8(iv).

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Replica field theories, Painlevé transcendents, and exact correlation functions. Phys. Rev. Lett. 89 (25), pp. (250201–1)–(250201–4).

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ISSN 0031-9007, Document, MathReview, ZentralBlatt

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§32.16.

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Rational solutions of the fifth Painlevé equation. Differential Integral Equations 7 (3-4), pp. 967–1000.

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ISSN 0893-4983, MathReview, ZentralBlatt

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§32.8(v).

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9: Bibliography P

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Evaluation of Fermi-Dirac Integral. In Nonlinear Numerical Methods and Rational Approximation (Wilrijk, 1987), A. Cuyt (Ed.), Mathematics and Its Applications, Vol. 43, pp. 435–444.

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MathReview, ZentralBlatt

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§25.18(i).

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The exact distribution of the Wald statistic. Econometrica 54 (4), pp. 881–895.

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ISSN 0012-9682, FullText, MathReview (Sadanori Konishi), ZentralBlatt

Referenced by:

§35.9.

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