Abstract
With the aid of Mullin-Rota＇s substitution rule, we show that the Sheffertypedifferential operators together with the delta operators D and D could be used toconstruct a pair of expansion formulas that imply a wide variety of summation formulasin the discrete analysis and combinatorics. A convergence theorem is establishedfor a fruitful source formula that implies more than 20 noted classical fomulas and identitiesas consequences. Numerous new formulas are also presented as illustrativeexamples. Finally, it is shown that a kind of lifting process can be used to producecertain chains of （∞m） degree formulas for m≥3 with m≡1 （mod 2） and m≡1 （mod3）, respectively.
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