Difference between revisions of "1Phi0(a;;z) as infinite product"
From specialfunctionswiki
(Created page with "==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]...") |
|||
| (2 intermediate revisions by the same user not shown) | |||
| Line 7: | Line 7: | ||
==References== | ==References== | ||
| − | * {{BookReference|Higher Transcendental Functions Volume I|1953| | + | * {{BookReference|Higher Transcendental Functions Volume I|1953|Arthur Erdélyi|author2=Wilhelm Magnus|author3=Fritz Oberhettinger|author4=Francesco G. Tricomi|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]] | ||
Latest revision as of 23:26, 3 March 2018
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: Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger and Francesco G. Tricomi: Higher Transcendental Functions Volume I ... (previous) ... (next): $4.8 (4)$
