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Analytic solutions of the quantum two-state problem in terms of the double-, bi- and tri-confluent Heun functions
T. A. Shahverdyan, T. A. Ishkhanyan, A. E. Grigoryan +1
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…
Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions
T. A. Ishkhanyan, Y. Pashayan-Leroy, M. R. Gevorgyan +2
Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the bico…
A series solution of the general Heun equation in terms of incomplete Beta functions
A. M. Manukyan, T. A. Ishkhanyan, M. V. Hakobyan +1
We show that in the particular case when a characteristic exponent of the singularity at infinity is zero the solution of the general Heun equation can be expanded in terms of the…
Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan
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…
Confluent hypergeometric expansions of the solutions of the double-confluent Heun equation
T. A. Ishkhanyan, V. A. Manukyan, A. H. Harutyunyan +1
Several expansions of the solutions of the double-confluent Heun equation in terms of the Kummer confluent hypergeometric functions are presented. Three different sets of these fun…
Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions
T. A. Ishkhanyan, A. M. Ishkhanyan
We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients…
New relations for the derivative of the confluent Heun function
V. A. Shahnazaryan, T. A. Ishkhanyan, T. A. Shahverdyan +1
The cases when the equation for the derivative of the confluent Heun function has only three singularities (in general, the equation has four such points) are examined. It is shown…