exact rational
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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 , where and 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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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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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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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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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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Rational Chebyshev approximations for the exponential integral
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Math. Comp. 22 (103), pp. 641–649.
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Rational Chebyshev approximations for the error function.
Math. Comp. 23 (107), pp. 631–637.
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Exact elliptic compactons in generalized Korteweg-de Vries equations.
Complexity 11 (6), pp. 30–34.
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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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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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Rational Chebyshev approximation for the Fermi-Dirac integral
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Solid–State Electronics 41 (5), pp. 771–773.
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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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Application of uniform asymptotics to the second Painlevé transcendent.
Arch. Rational Mech. Anal. 143 (3), pp. 241–271.
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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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Rational Chebyshev approximations for the Bickley functions
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Math. Comp. 32 (143), pp. 876–886.
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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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7: Bibliography I
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Centre for Experimental and Constructive Mathematics, Simon Fraser University, Canada.
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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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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Determinant structure of the rational solutions for the Painlevé IV equation.
J. Phys. A 31 (10), pp. 2431–2446.
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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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Rational solutions of the fifth Painlevé equation.
Differential Integral Equations 7 (3-4), pp. 967–1000.
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