Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 3 : pp. 260–282
Abstract
With the aid of Mullin-Rota's substitution rule, we show that the Sheffer-type differential operators together with the delta operators Δ and D could be used to construct a pair of expansion formulas that imply a wide variety of summation formulas in the discrete analysis and combinatorics. A convergence theorem is established for a fruitful source formula that implies more than 20 noted classical formulas and identities as consequences. Numerous new formulas are also presented as illustrative examples. Finally, it is shown that a kind of lifting process can be used to produce certain chains of (∞m) degree formulas for m≥3 with m≡1 (mod 2) and m≡1 (mod 3), respectively.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n3.5
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 3 : pp. 260–282
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Delta operator Sheffer-type operator (∞m) degree formula triplet lifting process.