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Second order differential equations with hypergeometric solutions of degree three

Published: 26 June 2013 Publication History

Abstract

Let L be a second order linear homogeneous differential equation with rational function coefficients. The goal in this paper is to solve L in terms of hypergeometric function 2F1(a,b;c|f) where f is a rational function of degree 3.

References

[1]
R. Debeerst, M. van Hoeij, W. Koepf: Solving Differential Equations in Terms of Bessel Functions, ISSAC'08 Proceedings, 39--46 (2008).
[2]
M. van Hoeij: An implementation for findingequivalence map, www.math.fsu.edu/~hoeij/files/equiv.
[3]
Q. Yuan, M. van Hoeij: Finding all Bessel type solutions for Linear Differential Equations with Rational Function Coefficients, ISSAC'2010 Proceedings, 37--44 (2010).
[4]
A. Bostan, F. Chyzak, M. van Hoeij, L. Pech: Explicit formula for the generating series of diagonal 3D rook paths, Seminaire Lotharingien de Combinatoire, B66a (2011).
[5]
R. Vidunas: Algebraic transformations of Gauss hypergeometric functions. Funkcialaj Ekvacioj, Vol 52 (Aug 2009), 139--180.
[6]
T. Fang, M. van Hoeij: 2-Descent for Second Order Linear Differential Equations, ISSAC'2011 Proceedings, 107--114 (2011).
[7]
J. Kovacic: An algorithm for solving second order linear homogeneous equations, J. Symbolic Computations, 2, 3--43 (1986).
[8]
M. van Hoeij, R. Vidunas: Belyi functions for hyperbolic hypergeometric-to-Heun transformations, arXiv:1212.3803.
[9]
M. van Hoeij, V. J. Kunwar: Hypergeometric solutions of second order differential equations with 5 non-removable singularities, (In Progress).
[10]
Z. X. Wang, D. R. Guo: Special Functions World Scientific Publishing Co. Pte. Ltd, Singapore, 1989.
[11]
V. J. Kunwar: An implementation for hypergeometric solution of second order differential equation with degree 3 rational function, www.math.fsu.edu/~vkunwar/hypergeomdeg3.
[12]
M. van Hoeij: Solving Third Order Linear Differential Equation in Terms of Second Order Equations, ISSAC'07 Proceedings, 355--360, 2007. Implementation: www.math.fsu.edu/~hoeij/files/ReduceOrder.
[13]
Q. Yuan: Finding all Bessel type solutions for Linear Differential Equations with Rational Function Coefficients, Ph.D thesis and implementation, available at www.math.fsu.edu/~qyuan(2012).
[14]
T. Fang: Solving Linear Differential Equations in Terms of Hypergeometric Functions by 2-Descent, Ph.D thesis and implementation, available at www.math.fsu.edu/~tfang (2012).

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  1. Second order differential equations with hypergeometric solutions of degree three

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    cover image ACM Conferences
    ISSAC '13: Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation
    June 2013
    400 pages
    ISBN:9781450320597
    DOI:10.1145/2465506
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    Published: 26 June 2013

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    Author Tags

    1. algorithms
    2. closed form solutions
    3. differential equations

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