Basic hypergeometric phi

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The basic hypergeometric series ${}_r\phi{}_s$ is defined by $${}_r \phi_s(a_1,a_2,\ldots,a_r; b_1,b_2,\ldots,b_s; z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(a_1;q)_k(a_2;q)_k \ldots (a_r;q)_k}{(b_1;q)_k (b_2;q)_k \ldots (b_s;q)_k} \dfrac{z^k}{(q;q)_k},$$ where $(a_1;q)_k$ denotes the q-shifted factorial.

Properties[edit]

Exponential e in terms of basic hypergeometric phi
1Phi0(a;;z) as infinite product

References[edit]

See Also[edit]

Hypergeometric pFq
Basic hypergeometric series psi