Concerning a General Source Formula and Its Applications

Abstract:

      Here presented is a further investigation on a general source formula (GSF) that has been proved capable of deducing more than 30 special formulas for series expansions and summations in the author's recent paper [On a pair of operator series expansions implying a variety of summation formulas. Anal. Theory Appl., 2015, 31(3): 260--282]. It is shown that the pair of series transformation formulas found and utilized by He, Hsu and Shiue [cf. Disc. Math., 2008, 308: 3427--3440] is also deducible from the GSF as consequences. Thus it is found that the GSF actually implies more than 50 special series expansions and summation formulas. Finally, several expository remarks relating to the $(\Sigma\Delta D)$ formula class are given in the closing section.