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1—10 of 30 matching pages
1: 36.2 Catastrophes and Canonical Integrals
2: Bibliography K
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Integral equations for special functions of Heun class.
Methods Appl. Anal. 3 (4), pp. 447–456.
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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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Rational solutions of the fifth Painlevé equation.
Differential Integral Equations 7 (3-4), pp. 967–1000.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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3: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice.
Phys. A 190 (3-4), pp. 346–362.
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4: Bibliography N
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Toda equation and its solutions in special functions.
J. Phys. Soc. Japan 65 (6), pp. 1589–1597.
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Solving equations exactly.
J. Res. Nat. Bur. Standards Sect. B 71B, pp. 171–179.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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5: Software Index
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6: Bibliography V
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A Mathieu equation for ships rolling among waves. I, II.
Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.
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On the growth of convergence radii for the eigenvalues of the Mathieu equation.
Math. Nachr. 192, pp. 239–253.
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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation.
Constr. Approx. 20 (1), pp. 39–54.
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Four remarks on eigenvalues of Lamé’s equation.
Anal. Appl. (Singap.) 2 (2), pp. 161–175.
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On the rational solutions of the second Painlevé equation.
Differ. Uravn. 1 (1), pp. 79–81 (Russian).
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7: Bibliography O
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Studies on the Painlevé equations. I. Sixth Painlevé equation
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Ann. Mat. Pura Appl. (4) 146, pp. 337–381.
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Studies on the Painlevé equations. II. Fifth Painlevé equation
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Japan. J. Math. (N.S.) 13 (1), pp. 47–76.
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Studies on the Painlevé equations. IV. Third Painlevé equation
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Funkcial. Ekvac. 30 (2-3), pp. 305–332.
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Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation.
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.
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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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8: Bibliography L
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Some differential equations and associated integral equations.
Quart. J. Math. (Oxford) 5, pp. 81–97.
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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Solutions to a generalized spheroidal wave equation: Teukolsky’s equations in general relativity, and the two-center problem in molecular quantum mechanics.
J. Math. Phys. 27 (5), pp. 1238–1265.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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The second Painlevé equation.
Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).
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9: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Algorithms for special integrals of ordinary differential equations.
J. Phys. A 29 (5), pp. 973–991.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Generalized elliptic integrals and modular equations.
Pacific J. Math. 192 (1), pp. 1–37.
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Integral equations and relations for Lamé functions.
Quart. J. Math. Oxford Ser. (2) 15, pp. 103–115.
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10: Errata
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Rearrangement
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Equation (15.6.8)
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Chapters 8, 20, 36
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Equation (22.16.14)
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Equation (36.10.14)
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22.16.14
Originally this equation appeared with the upper limit of integration as , rather than .
Reported 2010-07-08 by Charles Karney.
36.10.14
Originally this equation appeared with in the second term, rather than .
Reported 2010-04-02.