Novel Representation of the General Fuchsian and Heun Equations and their Solutions

Fiziev, Plamen

doi:10.18052/www.scipress.com/IFSL.7.11

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International Frontier Science Letters

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Novel Representation of the General Fuchsian and Heun Equations and their Solutions

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Abstract:

In the present article we introduce and study a novel type of solutions to the general Heun's equation. Our approach is based on the symmetric form of the Heun's differential equation yielded by development of the Papperitz-Klein symmetric form of the Fuchsian equations with an arbitrary number N≥4 of regular singular points. We derive the symmetry group of these equations which turns to be a proper extension of the Mobius group. We also introduce and study new series solutions of the proposed in the present paper symmetric form of the general Heun's differential equation (N=4) which treats simultaneously and on an equal footing all singular points.

Info:

Periodical:

International Frontier Science Letters (Volume 7)

Pages:

11-24

DOI:

https://doi.org/10.18052/www.scipress.com/IFSL.7.11

Citation:

P. Fiziev, "Novel Representation of the General Fuchsian and Heun Equations and their Solutions", International Frontier Science Letters, Vol. 7, pp. 11-24, 2016

Online since:

March 2016

Authors:

Plamen Fiziev

Keywords:

Fuchsian Equations, General Heun's Equation, Mobius Group, Papperitz-Klein Symmetric Form, Recurrence Relations, Solutions to the General Heun's Equation

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Creative Commons Attribution 4.0 International License

References:

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Cited By:

[1] M. Hortaçsu, "Heun Functions and Some of Their Applications in Physics", Advances in High Energy Physics, Vol. 2018, p. 1, 2018

DOI: https://doi.org/10.1155/2018/8621573