Ince’s limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable z, while the other is given by a series of modified Bessel functions and conv...

متن کامل

New solutions for the General, Confluent and Bi-Confluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfl...

متن کامل

New closed form solutions in terms of pFq for families of the General, Confluent and Bi-Confluent Heun differential equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfl...

متن کامل

Solutions for the General, Confluent and Biconfluent Heun equations and their connection with Abel equations

In a recent paper, the canonical forms of a new multi-parameter class of Abel differential equations, so-called AIR, all of whose members can be mapped into Riccati equations, were shown to be related to the differential equations for the hypergeometric 2F1, 1F1 and 0F1 functions. In this paper, a connection between the AIR canonical forms and the Heun General (GHE), Confluent (CHE) and Biconfl...

متن کامل

Integral relations for solutions of the confluent Heun equation

Abstract: Firstly, we construct kernels for integral relations among solutions of the confluent Heun equation (CHE). Additional kernels are systematically generated by applying substitutions of variables. Secondly, we establish integral relations between known solutions of the CHE that are power series and solutions that are series of special functions. Thirdly, by using one of the integral rel...

متن کامل

Ince’s limits for confluent and double-confluent Heun equations

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

منابع مشابه