STUDY OF A TYPE OF GENERALIZED BASIC HYPERGEOMETRIC SERIES

摘要

The aim of this paper is to examine the generalized basic hypergeometric series defined by f(x)=_(r+1)Φ_r[q~(-M),q~(b_1+m_1),q~(b_2+m_2),...,q~(b_r+m_r)q~(b_1),q~(b_2),...,q~(b_r);q,q~nx]M,m_1,m_2,...,m_r,n∈N, b_1,b_2,...,b_r≠0,-1,-2,..., 0 ＜ q ＜ 1, for this, the effects of the parameters b_j,m_j (j = 1,2,...r), q and n on the function f are studied, considering some examples and establishing for each one the following characteristics of f(x) : the polynomial that defines it, the roots of same and its set of positivily. Also, various graphics which show the behavior of the function are included.