# Hypergeometric expansions of the solutions of the general Heun equation governed by two-term recurrence relations for expansion coefficients

@article{Ishkhanyan2014HypergeometricEO, title={Hypergeometric expansions of the solutions of the general Heun equation governed by two-term recurrence relations for expansion coefficients}, author={T. A. Ishkhanyan and T. A. Shahverdyan and Artur M. Ishkhanyan}, journal={arXiv: Classical Analysis and ODEs}, year={2014} }

We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions the forms of which differ from those applied before. In general the coefficients of the expansions obey three-term recurrence relations. However, there exist a certain set of the parameters of the Heun equation for which the recurrence relation becomes two-term. The coefficients of the expansions are then explicitly expressed in…

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## 11 Citations

### Appell Hypergeometric Expansions of the Solutions of the General Heun Equation

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### Analytic solutions of the quantum two-state problem in terms of the double, bi- and triconfluent Heun functions

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We derive five classes of quantum time-dependent two-state models solvable in terms of the double confluent Heun functions, five other classes solvable in terms of the biconfluent Heun functions, and…

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A specific constant-amplitude periodic level-crossing model of the semi-classical quantum time-dependent two-state problem that belongs to a general Heun class of field configurations is presented.…

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### Quantum features of molecular interactions associated with time-dependent non-central potentials

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We consider the indices of coincidence for the binomial, Poisson, and negative binomial distributions. They are related in a simple manner to the Rényi entropy and Tsallis entropy. We investigate…

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