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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > Values at z=1 > For fixed a1, a2, b1





http://functions.wolfram.com/07.27.03.0021.01









  


  










Input Form





HypergeometricPFQ[{1, a, b}, {2, d}, 1] == ((d - 1)/((a - 1) (b - 1))) ((Gamma[d - 1] Gamma[1 + d - a - b])/(Gamma[d - a] Gamma[d - b]) - 1) /; Re[d - a - b] > -1 && a != 1 && b != 1 && c != 1










Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> d </mi> <mo> - </mo> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> &#8743; </mo> <mrow> <mi> a </mi> <mo> &#8800; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> b </mi> <mo> &#8800; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> c </mi> <mo> &#8800; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> <ci> a </ci> <ci> b </ci> </list> <list> <cn type='integer'> 2 </cn> <ci> d </ci> </list> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <and /> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <neq /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <neq /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <neq /> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29