Proof And Application Of Some Cubic Generalized Hypergeometric Series Identities

By means of the classical analytical tool "Abel's lemma on summation by parts",this thesis investigates systematically a cubic generalized hypergeometric series and its partial sum.Several transformation and summation formulae for this cubic series are established.These results not only generalize some known formulae,but also give a new cubic nonterminating 7F6-series summation formula.In the preface,the author briefly reviews the related concepts,development and research status of generalized hypergeometric series.The main research tool "Abel's lemma on summation by parts" is expounded in detail.In Chapter 2,a new cubic nonterminating 7F6-series summation formula with 3 free parameters is derived by means of the limiting case of Abel's lemma on summation by parts.In Chapter 3,the modified Abel's lemma on summation by parts with "remainder term" is employed to investigate a new cubic series Qn(a,b,c,d)which generalizes the last 7F6-series.A series of transformation formulae are established,which generalize some results due to Chu(1994).In Chapter 4,by means of the Abel lemma on summation by parts,some recurrence relations and transformations for Q(a,b,c,d)(the limiting case of Qn(a,b,c,d)when n??)are established.These results are used to obtain several infinite series extensions for circumference ratio ? further.Chapter 5 is the summary of the whole thesis and the prospect of future research work.