Difference between revisions of "1Phi0(a;;z) as infinite product"
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==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Basic hypergeometric phi|next= | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Basic hypergeometric phi|next=1Phi0(a;;z)1Phi0(b;;az)=1Phi0(ab;;z)}}: $4.8 (4)$ |
[[Category:Theorem]] | [[Category:Theorem]] | ||
[[Category:Unproven]] | [[Category:Unproven]] | ||
Revision as of 21:44, 17 June 2017
Theorem
The following formula holds: $${}_1\phi_0(a;;z)=\displaystyle\prod_{k=0}^{\infty} \dfrac{1-aq^kz}{1-q^kz},$$ where ${}_1\phi_0$ denotes basic hypergeometric phi.
Proof
References
- 1953: Harry Bateman: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.8 (4)$
