generalized%20integrals
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11: 36.5 Stokes Sets
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§36.5(ii) Cuspoids
… ►They generate a pair of cusp-edged sheets connected to the cusped sheets of the swallowtail bifurcation set (§36.4). … ►The first sheet corresponds to and is generated as a solution of Equations (36.5.6)–(36.5.9). … ►§36.5(iii) Umbilics
… ►§36.5(iv) Visualizations
…12: Bibliography I
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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines.
Z. Angew. Math. Mech. 75 (12), pp. 917–926.
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An integral which occurs in statistics.
Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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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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An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
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13: Bibliography S
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A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals.
Comput. Phys. Comm. 66 (2-3), pp. 271–275.
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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A method of generating integral relations by the simultaneous separability of generalized Schrödinger equations.
SIAM J. Math. Anal. 10 (4), pp. 823–838.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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14: Bibliography L
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Monotonicity properties of zeros of generalized Airy functions.
Z. Angew. Math. Phys. 39 (2), pp. 267–271.
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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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Generalized Riemann -function regularization and Casimir energy for a piecewise uniform string.
Phys. Rev. D 44 (2), pp. 560–562.
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15: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Première partie. La fonction de Riemann et les nombres premiers en général, suivi d’un Appendice sur des réflexions applicables à une formule donnée par Riemann.
Ann. Soc. Sci. Bruxelles 20, pp. 183–256 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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On Vandermonde’s theorem, and some more general expansions.
Proc. Edinburgh Math. Soc. 25, pp. 114–132.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities.
Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
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16: Bibliography G
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On the generalization of a method for computing Bessel function integrals.
J. Comput. Appl. Math. 6 (2), pp. 167–168.
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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On the computation of generalized Fermi-Dirac and Bose-Einstein integrals.
Comput. Phys. Comm. 74 (2), pp. 233–238.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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17: 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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Generalized Fermi-Dirac integrals—FD, FDG, FDH.
Comput. Phys. Comm. 39 (2), pp. 181–185.
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18: Bibliography W
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Caustics: Mathematical curves generated by light shined through rippled plastic.
Scientific American 249, pp. 146–153.
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Infinitely differentiable generalized logarithmic and exponential functions.
Math. Comp. 57 (196), pp. 723–733.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Some transformations of generalized hypergeometric series.
Proc. London Math. Soc. (2) 26 (2), pp. 257–272.
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The asymptotic expansion of the generalized Bessel function.
Proc. London Math. Soc. (2) 38, pp. 257–270.
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19: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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An improved calculation of the general elliptic integral of the second kind in the neighbourhood of
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Numer. Math. 25 (1), pp. 99–101.
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Tables of Generalized Exponential Integrals.
NPL Mathematical Tables, Vol. III, Her Majesty’s Stationery Office, London.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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20: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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Numerical calculation of a generalized complete elliptic integral.
Rev. Mod. Phys. 10, pp. 264–269.
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Integral transforms with generalized Legendre functions as kernels.
Compositio Math. 18, pp. 235–287.
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Numerical calculation of elliptic integrals and elliptic functions. III.
Numer. Math. 13 (4), pp. 305–315.
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On a generalization of Barton’s integral and related integrals of complete elliptic integrals.
Math. Proc. Cambridge Philos. Soc. 101 (1), pp. 1–5.
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