Numerically satisfactory solutions of Kummer recurrence relations

Pairs of numerically satisfactory solutions as for the three-term recurrence relations satisfied by the families of functions , , are given. It is proved that minimal solutions always exist, except when and z is in the positive or negative real axis, and that is minimal as whenever . The minimal sol...

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Bibliographic Details
Published in:Numerische Mathematik 2008-11, Vol.111 (1), p.109-119
Main Authors: Segura, Javier, Temme, Nico M.
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical analysis. Scientific computation
Numerical and Computational Physics
Sciences and techniques of general use
Simulation
Theoretical
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Summary:Pairs of numerically satisfactory solutions as for the three-term recurrence relations satisfied by the families of functions , , are given. It is proved that minimal solutions always exist, except when and z is in the positive or negative real axis, and that is minimal as whenever . The minimal solution is identified for any recurrence direction, that is, for any integer values of and . When the confluent limit , with fixed, is the main tool for identifying minimal solutions together with a connection formula; for , is the main tool to be considered.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-008-0175-5