inhomogeneous differential equations
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11—18 of 18 matching pages
11: 10.15 Derivatives with Respect to Order
12: Bibliography E
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Integral equations for Heun functions.
Quart. J. Math., Oxford Ser. 13, pp. 107–112.
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The Fuchsian equation of second order with four singularities.
Duke Math. J. 9 (1), pp. 48–58.
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Certain expansions of solutions of the Heun equation.
Quart. J. Math., Oxford Ser. 15, pp. 62–69.
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A catalogue of Sturm-Liouville differential equations.
In Sturm-Liouville theory,
pp. 271–331.
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The asymptotic behaviour of the inhomogeneous Airy function
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Math. Chronicle 12, pp. 99–104.
13: 9.13 Generalized Airy Functions
§9.13 Generalized Airy Functions
βΊ§9.13(i) Generalizations from the Differential Equation
… βΊare used in approximating solutions to differential equations with multiple turning points; see §2.8(v). … βΊAs … βΊ …14: Bibliography K
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Asymptotic behavior of the solutions of the Painlevé equation of the first kind.
Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).
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Rational solutions of the fifth Painlevé equation.
Differential Integral Equations 7 (3-4), pp. 967–1000.
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On differential equations for Sobolev-type Laguerre polynomials.
Trans. Amer. Math. Soc. 350 (1), pp. 347–393.
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An algorithm for solving second order linear homogeneous differential equations.
J. Symbolic Comput. 2 (1), pp. 3–43.
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Quantum-Theoretical Formalism for Inhomogeneous Graded-Index Waveguides.
Akademie Verlag, Berlin-New York.
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15: 9.10 Integrals
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9.10.1
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9.10.2
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9.10.3
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βΊLet be any solution of Airy’s equation (9.2.1).
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9.10.18
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16: Bibliography M
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Computation of inhomogeneous Airy functions.
J. Comput. Appl. Math. 53 (1), pp. 109–116.
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Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 215–237.
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On reducing the Heun equation to the hypergeometric equation.
J. Differential Equations 213 (1), pp. 171–203.
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On the choice of standard solutions for a homogeneous linear differential equation of the second order.
Quart. J. Mech. Appl. Math. 3 (2), pp. 225–235.
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An Introduction to the Fractional Calculus and Fractional Differential Equations.
A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York.
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17: Bibliography G
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The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals.
Ann. of Math. (2) 48 (4), pp. 785–826.
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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments.
ACM Trans. Math. Software 30 (2), pp. 145–158.
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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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Special classes of solutions of Painlevé equations.
Differ. Uravn. 18 (3), pp. 419–429 (Russian).
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Theory of Painlevé’s equations.
Differ. Uravn. 11 (11), pp. 373–376 (Russian).
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18: Bibliography B
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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations.
The Macmillan Co., New York.
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Coefficient functions for an inhomogeneous turning-point problem.
Mathematika 38 (2), pp. 217–238.
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Ordinary differential equations.
Fourth edition, John Wiley & Sons, Inc., New York.
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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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The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods.
John Wiley & Sons Ltd., Chichester.
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