We study the main umbral operators J , M and N associated with the Cayley continuants U^(ν)_n (x) and the generalized Sylvester continuants H^(ν)_n (x) = U^(ν+n)_n (x) . In particular, we obtain their representation in terms of the differential operator D_x and the shift operator E . Then, by using these representations, we obtain some combinatorial and differential identities for the continuants U^(ν)_n (x) and H ^(ν)_n (x) .
UMBRAL OPERATORS FOR CAYLEY AND SYLVESTER CONTINUANTS
Munarini E.
2022-01-01
Abstract
We study the main umbral operators J , M and N associated with the Cayley continuants U^(ν)_n (x) and the generalized Sylvester continuants H^(ν)_n (x) = U^(ν+n)_n (x) . In particular, we obtain their representation in terms of the differential operator D_x and the shift operator E . Then, by using these representations, we obtain some combinatorial and differential identities for the continuants U^(ν)_n (x) and H ^(ν)_n (x) .File in questo prodotto:
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