Mathematical Proceedings of the Cambridge Philosophical Society · 1981 · 24 citations · 1 references
Natural SciencesMathematicsAlgebraDifferential EquationsNumber TheoryArithmetic GeometryDifference EquationsGenerating FunctionsAlgebraic Generating FunctionsChebyshev PolynomialsGegenbauer PolynomialsLinear Difference EquationsRational Generating Functions
The Fibonacci and Lucas polynomials F n ( z ) and L n ( z ) are denned. These reduce to the familiar Fibonacci and Lucas numbers when z = 1. The polynomials are shown to satisfy a second order linear difference equation. Generating functions are derived, and also various simple identities, and relations with hypergeometric functions, Gegenbauer and Chebyshev polynomials.
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