Generalized hypergeometric function: Difference between revisions

Revision as of 08:53, 14 February 2023

Revision as of 08:54, 14 February 2023

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===The series ₃''F''₂===

The function

::<math>\operatorname{Li}_2(x) = \sum_{n>0}\,{x^n}{n^{-2}} = x \; {}_3F_2(1,1,1;2,2;x)</math> is the [[dilogarithm]]<ref>{{cite web|last=Candan|first=Cagatay|title=A Simple Proof of F(1,1,1;2,2;x)=dilog(1-x)/x

::<math>\operatorname{Li}_2(x) = \sum_{n>0}\,{x^n}{n^{-2}} = x \; {}_3F_2(1,1,1;2,2;x)</math>

::<math>\operatorname{Li}_2(x) = \sum_{n>0}\,{x^n}{n^{-2}} = x \; {}_3F_2(1,1,1;2,2;x)</math> is the [[dilogarithm]]<ref>{{cite web|last=Candan|first=Cagatay|title=A Simple Proof of F(1,1,1;2,2;x)=dilog(1-x)/x

|url=http://www.eee.metu.edu.tr/~ccandan/pub_dir/hyper_rel.pdf}}</ref>

The function

::<math>Q_n(x;a,b,N)= {}_3F_2(-n,-x,n+a+b+1;a+1,-N+1;1)</math> is a [[Hahn polynomial]].

is a [[Hahn polynomial]].

===The series ₄''F''₃===