Integration Sequences of Jacobsthal and Jacobsthal-Lucas Polynomials

Piero Filipponi and Alwyn F. Horadam

A chapter in Applications of Fibonacci Numbers, 1999, pp 129-139 from Springer

Abstract: Abstract Here we are concerned with the Jacobsthal polynomials J n(x) and the Jacobsthal-Lucas polynomials j n(x) (e.g., see [4] and [5]) which are a natural extension of the Jacobsthal numbers J n and the Jacobsthal-Lucas numbers j n which, in turn, have been investigated in [3]. These polynomials are defined by the second-order recurrence relations $$J_{n+2}(x) = J_{n+1}(x)+2xJ_n(x), [J_0(x)=0, J_1(x)=1]$$ and $$j_{n+2}(x) = j_{n+1}(x)+2xj_n(x), [j_0(x)=2,j_1(x)=1]$$ respectively, where x is an indeterminate. Since throughout this paper we shall make use of the notation and the formulas found in [4], the reader is assumed to be aware of its contents.

Keywords: 11B37; 11B83; 26A06 (search for similar items in EconPapers)
Date: 1999
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DOI: 10.1007/978-94-011-4271-7_13

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