jacobsthal polynomial

Input interpretation

Jacobsthal polynomial

Definition

The Jacobsthal polynomials are the W-polynomial obtained by setting p(x) = 1 and q(x) = 2x in the Lucas polynomial sequence. The first few Jacobsthal polynomials are J_1(x) | = | 1 J_2(x) | = | 1 J_3(x) | = | 1 + 2x J_4(x) | = | 1 + 4x J_5(x) | = | 4x^2 + 6x + 1, Jacobsthal polynomials satisfy J_n(1) = J_n where J_n is a Jacobsthal number.
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Related terms

Jacobsthal-Lucas polynomial | Jacobsthal number

Subject classifications

MathWorld

special polynomials

MSC 2010

12E10 | 33-XX

Associated person

Ernst Erich Jacobsthal
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