The Q-Kummer Sum And Q-Operators

The operator approach has a very important and extensive influence on the development of basic hypergeometric series.This thesis reviews the introduction and development of the concepts of q-differential operators,lists and derives some operator formulas.We apply them to the deformations of the q-Kummer summation to derive all possible transformation formulas and summation formulas,and get some identities containing only q.In the first chapter,the basic knowledge and its history are introduced and the identities that will be used later are given.In the second chapter,some new operator formulas of E(bθ)are derived,and then E(bθ)acts on the deformations of the q-Kummer summation to obtain a series of identities containing only q.In the third chapter,some formulas for 1φ0(c;-;q,-bθ)are deduced and a summation formula for a nonterminating 2φ1 series is obtained,then the relevant 1φ0(c;-;q,-bθ)operator formulas acted upon in the variation of the q-Kummer sum,and finally some identities containing only q are obtained.In the fourth chapter,the main content of this thesis is summarized,and the direction of further research is given.