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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:
Mar 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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Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

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