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1: 3.8 Nonlinear Equations
2: 28 Mathieu Functions and Hill’s Equation
Chapter 28 Mathieu Functions and Hill’s Equation
…3: 20 Theta Functions
Chapter 20 Theta Functions
…4: 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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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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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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Asymptotic approximations for the Jacobi and ultraspherical polynomials, and related functions.
Methods Appl. Anal. 6 (3), pp. 21–56.
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5: 27.15 Chinese Remainder Theorem
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►Their product has 20 digits, twice the number of digits in the data.
…These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result , which is correct to 20 digits.
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►Details of a machine program describing the method together with typical numerical results can be found in Newman (1967).
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6: 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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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Pfaff’s method II: Diverse applications.
J. Comput. Appl. Math. 68 (1-2), pp. 15–23.
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7: Bibliography B
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Some solutions of the problem of forced convection.
Philos. Mag. Series 7 20, pp. 322–343.
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Bessel functions and modular relations of higher type and hyperbolic differential equations.
Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.
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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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On mean convergence of extended Lagrange interpolation.
J. Comput. Appl. Math. 43 (1-2), pp. 19–35.
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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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A method for evaluating certain Bessel integrals.
Z. Angew. Math. Phys. 30 (4), pp. 722–723.
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Method for evaluation of zeros of Bessel functions.
J. Inst. Math. Appl. 11, pp. 57–72.
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9: Staff
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William P. Reinhardt, University of Washington, Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, Chaps. 20, 22, 23
Gerhard Wolf, University of Duisberg-Essen, Chap. 28
William P. Reinhardt, University of Washington, for Chaps. 20, 22, 23
Peter L. Walker, American University of Sharjah, for Chaps. 20, 22, 23
10: 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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