Q-Gosper Algorithm And Simple Bailey Pairs

We present a method of constructing simple Bailey pairs based on the q-Gosper algorithm.For a given form of q-hypergeometric terms,we use the q-Gosper algorithm to determine the unknown parameters in them so that they are Gosper-summable,resulting in the corresponding simple Bailey pairs.We illustrate the method by determining Gosper-summable q-hypergeometric terms of the form(a;q)k/(q;q)kzk.We further give some simple Bailey pairs in more complicated forms.As applications,we derive some summation and transformation formulas for q-series.In chapter 1,we review the history of basic hypergeometric series and Bailey pairs.In chapter 2,we construct possible Gosper-summable q-hypergeometric terms of the form tk=(a;q)k/(q;q)kzk.And then we get some simple Bailey pairs(?n,?n)by the formula zn+1-z0=?n,tn=?n.At last,we obtain some basic hypergeometric series identities.In chapter 3,we consider the summability of more q-hypergeometric terms,and get some simple Bailey pairs.By substituting these simple Bailey pairs into some known identities involving simple Bailey pairs,we obtain some summation and transformation formulas of q-series.