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.

Periodical:

International Frontier Science Letters (Volume 7)

Pages:

11-24

DOI:

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:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

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