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 [O...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.展开更多
文摘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.
