Some Special Solutions of Biconfluent and Triconfluent Heun Equations in Elementary Functions by Extended Nikiforov-Uvarov Method

We report some special solutions of biconfluent Heun equation and triconfluent Heun equation via extended Nikiforov-Uvarov (NU) method which is developed by changing the boundary conditions of NU method [8]. We demonstrate that eigenvalue solutions of these confluent forms of Heun equation can be achieved exactly. Furthermore we give eigenvalue solution of a two-electron quantum dot model problem as a physical application of extended NU method.