On Certain Solutions for Confluent and Double-Confluent Heun Equations

Details On Certain Solutions for Confluent and Double-Confluent Heun Equations On Certain Solutions for Confluent and Double-Confluent Heun Equations

2008-07-14

arxiv.org/abs/0807.2219v3

Physics

Mathematical Physics

In the present version (v3) we corrected Ref [3]. A slightly different form of this manuscript, entitled "Solutions for conflu

Scientific paper

This paper examines some solutions for confluent and double-confluent Heun equations. In the first place, we review two Leaver's solutions in series of regular and irregular confluent hypergeometric functions for the confluent equation and introduce an additional expansion in series of irregular confluent hypergeometric functions. Then, we find the conditions under which one of these solutions can be written as a linear combination of the others. In the second place, by means of limiting procedures we generate solutions for the double-confluent equation as well as for special limits of both the confluent and double-confluent equations. Finally, we present problems which are ruled by each of these four equations and establish relations among Heun equations and quasi-exactly solvable problems.

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