Abel’s Lemma on Summation by Parts and q-Series Transformation and Summation Formulae
|School||Dalian University of Technology|
|Keywords||Abel summation by Lemma Basic hypergeometric series Complementary relationship Transformation formula Summation formula|
Use of Abel summation by Lemma paper systematically studies the basic hypergeometric series part , to get a series of series about the the columns balance of (well-poised) , second series , three series , four series as well as some other basic hypergeometric series of transformation and summation formulas main content summarized as follows : Introduction section details the basic hypergeometric series development history as well as the main way of thinking -Abel summation method , and column equilibrium stages example illustrates the efficacy of this method in the basic hypergeometric series study . second chapter use of the Abel summation by Lemma secondary basic hypergeometric series complementary relationship as well as the series of column balance between transformation formula . accordingly , the authors regain Chu (1995) , and Gessel - Stanton ( 1983 ) use of inversion techniques to obtain the termination of the series summation formulas and Gasper (1989) and Rahman (1993) uses a series rearrangement method of non- terminated series transformation and summation formulas third chapter the use of the Abel summation Lemma study three basic hypergeometric series part of the establish complementary relationship on three stages , as well as the transformation formula with column equilibrium stages . two formulas not only promote Chu ( 1993 ) , Gasper ( 1989 ) and Gasper-Rahman (1990) results , and export part of the new basic hypergeometric series identities . fourth chapter aims to use Abel summation by Lemma study two pairs the dual four basic hypergeometric series part and respect to the first pair of series to each other , with similar results in the second and third stages , similar series complementary relationship and their balanced and column series between transformation formula ; for the second pair , the authors will be given six unusual transformation formula , including a series or twice or three times as well as another four series transform Chapter Abel segment summing Lemma bilateral ultimate form of public bilateral promotion of the establishment of the following well-known summation formula : q-Bailey q-Gauss summation formula of Andrews ( 1973 ) , Andrews (1976) , and Jain (1981) on the Watson and Whipple the formula two q- analog of the generalized formula can be seen as M.Jackson (1949) of 3 sub > H 3 sub > - series identities complete q - analog .