$U(n+1)$ Generalizations of the Kalnins-Miller $_3\phi_2$ and Sears $_4\phi_3$ Transformations

Zhizheng Zhang
Department of Mathematics, Luoyang Teachers' College, Luoyang 471022, P. R. China
Abstract     Full Text  PPT

In this report, from several $U(n+1)$ generalizations of $q$-Gauss summation theorem, we obtain some $U(n+1)$ generalizations of the Kalnins-Miller $_3\phi_2$ and Sears $_4\phi_3$ transformations. The course is that: multiple $q$-Chu-Vandermonde summations $\rightarrow$ the multiple Kalnins and Miller's transformations $\rightarrow$ the multiple
Sears $_4\phi_3$ transformations $\rightarrow$ the multiple Kummer and
Hall transformations $_3\phi_2$.