Q-analogue Of Several Combinatorial Identities And U(N+1) Extensions

In this thesis, we mainly obtain the q-analogue of several combinatorial identitiesinvolving binomial coefcients and harmonic numbers and several U(n+1) extensions ofbasic hypergeometric series.In Chapter1, we mainly introduce the basic hypergeometric series, multiple basichypergeometric series and some main notations, definitions.In Chapter2, we establish q-analogue of some identities with products of q-harmonicnumbers and reciprocals of q-binomial coefcients.In Chapter3, we get some U(n+1) basic hypergeometric series equations by usingCarlitz's inversion.