Liouville%20transformation%20for%20differential%20equations
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11—20 of 614 matching pages
11: 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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Problem 72-21, Laplace transforms of Airy functions.
SIAM Rev. 15 (4), pp. 796–798.
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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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An extended class of orthogonal polynomials defined by a Sturm-Liouville problem.
J. Math. Anal. Appl. 359 (1), pp. 352–367.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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12: Bibliography L
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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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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Higher monotonicity properties of certain Sturm-Liouville functions. III.
Canad. J. Math. 22, pp. 1238–1265.
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Higher monotonicity properties of certain Sturm-Liouville functions. IV.
Canad. J. Math. 24, pp. 349–368.
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Higher monotonicity properties of certain Sturm-Liouville functions..
Acta Math. 109, pp. 55–73.
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13: 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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14: 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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15: 31.2 Differential Equations
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►All other homogeneous linear differential equations of the second order having four regular singularities in the extended complex plane, , can be transformed into (31.2.1).
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-Homotopic Transformations
… ►Homographic Transformations
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►There are automorphisms of equation (31.2.1) by compositions of -homotopic and homographic transformations. …16: Bibliography P
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A Kummer-type transformation for a hypergeometric function.
J. Comput. Appl. Math. 173 (2), pp. 379–382.
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Bounds for ratios of modified Bessel functions.
Integral Transform. Spec. Funct. 9 (4), pp. 293–298.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Fourier Series and Integral Transforms.
Cambridge University Press, Cambridge.
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Numerical Solution of Sturm-Liouville Problems.
Monographs on Numerical Analysis, The Clarendon Press, Oxford University Press, New York.
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17: 29.2 Differential Equations
§29.2 Differential Equations
►§29.2(i) Lamé’s Equation
… ►§29.2(ii) Other Forms
… ►Equation (29.2.10) is a special case of Heun’s equation (31.2.1).18: 32.2 Differential Equations
§32.2 Differential Equations
►§32.2(i) Introduction
►The six Painlevé equations – are as follows: … ►be a nonlinear second-order differential equation in which is a rational function of and , and is locally analytic in , that is, analytic except for isolated singularities in . … ►They are distinct modulo Möbius (bilinear) transformations …19: 3.8 Nonlinear Equations
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►The equation to be solved is
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►This is useful when satisfies a second-order linear differential equation because of the ease of computing .
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►For describing the distribution of complex zeros of solutions of linear homogeneous second-order differential equations by methods based on the Liouville–Green (WKB) approximation, see Segura (2013).
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►Consider and .
We have and .
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