Expansion Formulas for q-series and Applications

From a well-known form of the power series expansion of f (b) , the certain unilateral and series of bilateral and Series conversion formula , including ₆ φ ₅ and _{3 < / sub> ψ 3 < / sub> conversion formula 6 φ 5 and 5 < / sub > ψ 5 conversion formula , which gives the well - poised 6 φ 5 < / sub > Sum new proof of the formula . these conversion formulas limited form includes not only the famous theorem q- analog Dixon , also received a similar Dixon theorem q- analog formula using the power series expansion , we also get some classic summation formula 1 φ 1 and the conversion formula between 1 φ 1 < / sub > 2 φ 2 < / sub> and 2 < / sub> φ conversion formula between 2 .}