Van%20Vleck%20theorem%20for%20continued%20fractions
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1: 1.12 Continued Fractions
2: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Zeros of Stieltjes and Van Vleck polynomials and applications.
J. Math. Anal. Appl. 110 (2), pp. 327–339.
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Characterization theorems for orthogonal polynomials.
In Orthogonal Polynomials (Columbus, OH, 1989),
NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 294, pp. 1–24.
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Zeros of Stieltjes and Van Vleck polynomials.
Trans. Amer. Math. Soc. 252, pp. 197–204.
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3: Staff
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Tom H. Koornwinder, Universiteit van Amsterdam, Chap. 18
William P. Reinhardt, University of Washington, Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23
William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23
4: 20 Theta Functions
Chapter 20 Theta Functions
…5: Bibliography V
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Calculation of spheroidal wave functions.
J. Acoust. Soc. Amer. 51, pp. 414–416.
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Accurate calculation of the modified Mathieu functions of integer order.
Quart. Appl. Math. 65 (1), pp. 1–23.
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Mathieu and Spheroidal Wave Functions: Fortran Programs for their Accurate Calculation
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Light Scattering by Small Particles.
John Wiley and Sons. Inc., New York.
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Multiple Light Scattering.
Vol. 1, Academic Press, New York.
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6: 27.15 Chinese Remainder Theorem
§27.15 Chinese Remainder Theorem
… ►This theorem is employed to increase efficiency in calculating with large numbers by making use of smaller numbers in most of the calculation. …Their product has 20 digits, twice the number of digits in the data. By the Chinese remainder theorem each integer in the data can be uniquely represented by its residues (mod ), (mod ), (mod ), and (mod ), respectively. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits. …7: Bibliography D
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Integralen voor de -functie van Riemann.
Mathematica (Zutphen) B5, pp. 170–180 (Dutch).
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Computing Riemann theta functions.
Math. Comp. 73 (247), pp. 1417–1442.
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Computing Riemann matrices of algebraic curves.
Phys. D 152/153, pp. 28–46.
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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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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8: Bibliography G
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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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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Matrix Computations.
3rd edition, Johns Hopkins University Press, Baltimore, MD.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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Inductance Calculations.
Van Nostrand, New York.
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9: 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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Hill’s Equation.
Interscience Tracts in Pure and Applied Mathematics, No. 20, Interscience Publishers John Wiley & Sons, New York-London-Sydney.
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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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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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