The modern definition of the q-hypergeometric function is _r ϕ_s[α_1, α_2, ..., α_r β_1, ..., β_s;q, z] congruent sum_(n = 0)^∞ ((α_1 ;q)_n (α_2 ;q)_n ...(α_r ;q)_n)/((β_1 ;q)_n ...(β_s ;q)_n) z^n/(q;q)_n [(-1)^n q^(n 2)]^(1 + s - r) , where (n 2) = 1/2 n(n - 1) is a binomial coefficient and (a;q)_n is a q-Pochhammer symbol. This is the version of the q-hypergeometric function implemented in the Wolfram Language as QHypergeometricPFQ[{a1, ..., ar}, {b1, ..., bs}, q, z].
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