Ince's limits for confluent and double-confluent Heun equations
- Instituto de Cosmologia, Relatividade e Astrofisica (ICRA-BR), Centro Brasileiro de Pesquisas Fisicas (CBPF), Rua Dr. Xavier Sigaud, 150 - 22290-180 - Rio de Janeiro, RJ (Brazil)
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 converges for vertical bar z vertical bar > vertical bar z{sub 0} vertical bar, where z{sub 0} denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when z{sub 0} tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schroedinger equation for inverse fourth- and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.
- OSTI ID:
- 20699621
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 46; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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