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Jacobsthal Polynomial

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JacobsthalPolynomial

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
(1)
J_2(x)=1
(2)
J_3(x)=1+2x
(3)
J_4(x)=1+4x
(4)
J_5(x)=4x^2+6x+1,
(5)

Jacobsthal polynomials satisfy

J_n(1)=J_n
(6)

where J_n is a Jacobsthal number.

See also

Jacobsthal-Lucas Polynomial, Jacobsthal Number

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References

Djordjevic, G. B. "Jacobsthal Polynomials." Fib. Quart. 38, 239, 2000.Filipponi, P. and Horadam, A. F. "Jacobsthal and Jacobsthal-Lucas Polynomials." Proc. Int. Conf. Fib. Numb. Appl., Vol. 8, p. 129, 1999.Hoggatt, V. E. Jr. and Bicknell-Johnson, M. "Arrays for Jacobsthal and Fibonacci Polynomials." bf 16, 385, 1978.Horadam, A. F. and Filipponi, P. "Fibonacci and Lucas Polynomials." Proc. Int. Conf. Fib. Numb. Appl., Vol. 5, p. 317, 1993.Jacobsthal, P. "Fibonaccische Polynome und Kreisteilungsgleichungen." Sitzungsber. Berliner Math. Gesell. 17, 43-57, 1919-1920.Swamy, M. N. S. "Jacobsthal Polynomials, A." Fib. Quart. 37, 141, 1999.

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Jacobsthal Polynomial

Cite this as:

Weisstein, Eric W. "Jacobsthal Polynomial." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/JacobsthalPolynomial.html

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