RIS ID
73437
Abstract
This paper generalizes a result of Gerdemann to show (with slight variations in some special cases) that, for any real number m and Horadam function Hn(A, B, P,Q), mHn(A, B, P, Q) = i=h k∑(t,Hn+i(A, B, P, Q)), for two consecutive values of n, if and only if, m= i=h k∑ (tiai)= i=h k∑ (t ibi) where a =(P+(P2-4Q) 1/2)/2 and b = (P-(P2-4Q) 1/2)/2. (Horadam functions are defined by: H 0(A, B, P, Q) = A, H1(A,B,P,Q) = B, Hn+1(A, B, P,Q) = PHn(A,B, P,Q)-QHn-1(A, B, P,Q).) Further generalizations to the solutions of arbitrary linear recurrence relations are also considered.
COinS
Publication Details
Bunder, M. W. (2012). Horadam functions and powers of irrationals. Fibonacci Quarterly, 50 (4), 304-312