We give a generalization of the identity proved by J.Worpitzky, by expressing each power $x^n$ as a linear combination of the images of $beta_m$ under the powers of the shift operator E. We encode the coefficients of these linear combinations in a 3-dimensional array - the Eulerian octant - and we find recurrences formulae, explicit expressions and generating functions for its entries.
G. Nicoletti, D. Ritelli, M. Silimbani (2006). A 3-dimensional Eulerian array. ANNALI DELL'UNIVERSITÀ DI FERRARA. SEZIONE 7: SCIENZE MATEMATICHE, Volume 52, 107-126.
A 3-dimensional Eulerian array
NICOLETTI, GIORGIO;RITELLI, DANIELE;SILIMBANI, MATTEO
2006
Abstract
We give a generalization of the identity proved by J.Worpitzky, by expressing each power $x^n$ as a linear combination of the images of $beta_m$ under the powers of the shift operator E. We encode the coefficients of these linear combinations in a 3-dimensional array - the Eulerian octant - and we find recurrences formulae, explicit expressions and generating functions for its entries.File in questo prodotto:
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