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Full-Text Articles in Mathematics
Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer
Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer
Mathematics Faculty Publications
No abstract provided.
When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik
When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik
Mathematics Faculty Publications
We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, …