Concerning a General Source Formula and Its Applications
Author(s): Leetsch C.HSU, School of Mathematical Sciences, Dalian University of Technology
Pages: 505-514
Year: 2016 Issue: 5
Journal: Journal of Mathematical Research and Exposition
Keyword: Sheffer-type operator; source formula; triplet; (Σ?D) class;
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(Σ?D) formula class are given in the closing section.
Pages: 505-514
Year: 2016 Issue: 5
Journal: Journal of Mathematical Research and Exposition
Keyword: Sheffer-type operator; source formula; triplet; (Σ?D) class;
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(Σ?D) formula class are given in the closing section.
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