TY - JOUR AU - Sadeghi, J. AU - Vaezi, A. AU - Larijani, F. PY - 2016 TI - The Heun Equation and Generalized Sl(2) Algebra JO - Journal of Mathematics and Computer Science SP - 77-80 VL - 16 IS - 1 AB - In this paper, first we introduce the Heun equation. In order to solve such equation we show the generators of generalized \(sl(2)\). Second, we arrange the Heun equation in terms of new operators formed of generalized \(sl(2)\) generators and it's commutator relation. Here, instead of \(J^+(r), J^-(r)\) and \(J^0\) we use the \(P^+(r), P^-(r)\) and \(P^0(r)\) as operators of generalized sl(2) algebra. This correspondence gives us opportunity to arrange the parameters \(\alpha\) and \(\beta\) in \(P^0(r)\). Also, the commutator of such operators leads us to have generalized \(sl(2)\) algebra. Also, we obtain the Casimir operators and show that it corresponds to \(P^+, P^-\) and some constants. These operators lead to deform the structure of generalized \(sl(2)\) algebra in the Heun equation. Finally, we investigate the condition for exactly and quasi-exactly solvable system with constraint on the corresponding operators \(P^+\) and \(P^-\). SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.016.01.08 DO - 10.22436/jmcs.016.01.08 ID - Sadeghi2016 ER - TY - JOUR TI - Formes canoniques des equations confluentes de l'equation de Heun AU - A. Decarreau AU - M. C. Dumont-Lepage AU - P. Maroni AU - A. Robert AU - A. Ronveaux JO - Ann. Soc. Sci. Bruxelles PY - 1978 DA - 1978// VL - 92 ID - Decarreau1978 ER - TY - JOUR TI - Sur les equations confluentes de l'equation de Heun AU - A. Decarreau AU - P. Maroni AU - A. Robert JO - Ann. Soc. Sci. Bruxelles PY - 1978 DA - 1978// VL - 92 ID - Decarreau1978 ER - TY - JOUR TI - On some solutions to generalized spheroidal wave equations and applications AU - B. D. B. Figueiredo JO - J. Phys. A PY - 2002 DA - 2002// VL - 35 ID - Figueiredo2002 ER - TY - JOUR TI - Ince's limits for confluent and double-confluent Heun equations AU - B. D. B. Figueiredo JO - J. Math. Phys. PY - 2005 DA - 2005// VL - 46 ID - Figueiredo2005 ER - TY - JOUR TI - Generalized spheroidal wave equation and limiting cases AU - B. D. B. Figueiredo JO - J. Math. Phys. PY - 2007 DA - 2007// VL - 48 ID - Figueiredo2007 ER - TY - JOUR TI - On Fuchsian differential equations reducible to hypergeometric equation by linear transformations AU - T. Kimura JO - Funkcial. Ekvac. PY - 1970/71 DA - 1970/71// VL - 13 ID - Kimura1970/71 ER - TY - JOUR TI - Solutions to a generalized spheroidal wave equation: Teukolsky's equations in general relativity, and the two-center problem in molecular quantum mechanics AU - E. W. Leaver JO - J. Math. Phys. PY - 1986 DA - 1986// VL - 27 ID - Leaver1986 ER - TY - BOOK TI - Introduction to the theory of linear differential equations AU - E. G. C. Poole PB - Dover Publications PY - 1936 DA - 1936// CY - New York ID - Poole1936 ER - TY - BOOK TI - Heuns Differential Equations AU - A. Ronveaux PB - Oxford University Press PY - 1995 DA - 1995// CY - New York ID - Ronveaux1995 ER - TY - JOUR TI - A generalised spheroidal wave equation AU - A. H. Wilson JO - proc. Roy. Soc. London PY - 1928 DA - 1928// VL - 118 ID - Wilson1928 ER - TY - JOUR TI - The ionised hydrogen molecule AU - A. H. Wilson JO - Proc. Roy. Soc. PY - 1928 DA - 1928// VL - 118 ID - Wilson1928 ER -