On the Values Si defined by the recursion S(i+1)=ui.S(i)+vi.S{i-1) (Russian)
B. Buchberger
Communications of the Joint Institute for Nuclear Research, Dubna, Soviet Union,
No P5-5789, May 1971, 12 pages.
ABSTRACT:
We derive a closed form representation of the solutions of linear recursions
over the natural numbers of the form
S(i+1)=ui.S(i)+vi.S{i-1)
vor given ui and vi. The representation involves the sum and product quantifiers
and some elementary functions on the natural numbers.
We apply the representation formula for deriving an explicit formula for the inverse
matrix of a tridiagonal matrix, which in fact constitutes an efficient method for the
inversion.