Difference between revisions of "1Phi0(a;;z) as infinite product"

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(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]...")
 
 
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==References==
 
==References==
* {{BookReference|Higher Transcendental Functions Volume I|1953|Harry Bateman|prev=Basic hypergeometric series phi|next=findme}}: $4.8 (4)$
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* {{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