RT Conference Proceedings
T1 On the stability of recurrence relations for hypergeometric functions
A1 Deaño Cabrera, Alfredo
A1 Segura, Javier
AB We consider the three term recurrence relations y_n+1 + a_n y_n + b_n y_n-1 = 0 satisfied simultaneously by confluent hypergeometric functions M(a+kn; c+mn; x) and U(a+kn; c+mn; x) (up to normalizations not depending on x). The parameters a, c, x are fixed and k,m = 0,±1. The existence of minimal solutions when n -> ∞ is a crucial piece of information when we intend to usea recurrence relation for computation. However, in some cases the behavior of the solutions for moderate values of n can be opposite to the asymptotic behaviour. We provide numerical examples of this phenomenon, already noted by W. Gautschi in the case (k,m) = (1,1), both for the recurrence relations and for the associated continued fractions.
PB Wiley VCH
SN 3-527-40652-2
YR 2005
FD 2005
LK https://hdl.handle.net/10016/6657
UL https://hdl.handle.net/10016/6657
LA eng
NO 4 pages, no figures.-- MSC2000 codes: 33C15, 33F05, 40A15.-- Running title: "Recurrences and continued fractions for Kummer functions".
NO Contributed to: ICNAAM 2005: Official conference of the European Society of Computational Methods in Sciences and Engineering (Rhodes, Greece, Sep 16-20, 2005).
NO Zbl#: Zbl 1086.33007
DS e-Archivo
RD 17 jul. 2024