Polynomial or Near-Polynomial solutions of Some Function Equations
Abstract
The functional equation G (z) G (Az + B) = G (Cz2 + Dz + E) is examined in two respects : ( i ) if the functional equation has a near-polynomial real solution in real variable, then this nearness can be determined, ( ii ) if E = 0 and A ≠ 0 , then the polynomial solution takes the form ( Cz / A)n.
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