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Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation

2002

Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.

Matrix difference equationFibonacci numberHermite polynomialsDifferential equationMathematical analysisMathematicsofComputing_NUMERICALANALYSISCharacteristic equationStatistical and Nonlinear PhysicsDifference equation matrix calculations Fibonacci sequence.Homogeneous differential equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONLinear difference equationMathematical PhysicsVariable (mathematics)MathematicsReports on Mathematical Physics
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