Relation of Boubaker Polynomials to Dickson Polynomials

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Theorem

The Boubaker polynomials $B_n$ are linked to the Dickson polynomials by the relations:

$B_{n+1} \left({x}\right) B_{n+j} \left({x}\right) - B_{n+j+1} \left({x}\right) B_n \left({x}\right) = \left({3 x^2 + 4}\right) D_{n+1} \left({x, \dfrac 1 4}\right)$
$B_n \left({x}\right) = D_n \left({2x, \dfrac 1 4}\right) + 4 D_{n-1} \left({2 x, \dfrac 1 4}\right)$


Proof


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