@Article{ATA-31-260,
author = {L. C. Hsu},
title = {On a Pair of Operator Series Expansions Implying a Variety of Summation Formulas},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {31},
number = {3},
pages = {260--282},
abstract = {<p style="text-align: justify;">With the aid of Mullin-Rota&#39;s substitution rule, we show that the Sheffer-type differential operators together with the delta operators $\Delta$ 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 $(\infty^m)$ degree formulas for $m\geq 3$ with $m\equiv 1$ (mod 2) and $m\equiv 1$ (mod 3), respectively.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2015.v31.n3.5},
url = {http://global-sci.org/intro/article_detail/ata/4639.html}
}