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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 a3, b2





http://functions.wolfram.com/07.27.03.0056.01









  


  








Input Form





HypergeometricPFQ[{1, 2, c}, {3, e}, 1] == ((2 (e - 2) (e - 1))/((c - 2) (c - 1))) (PolyGamma[e - 2] - PolyGamma[e - c]) - (2 (e - 1))/(c - 1) /; c != 1 && c != 2 && Re[e - c] > 0








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> e </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> c </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> c </mi> <mo> &#8800; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> c </mi> <mo> &#8800; </mo> <mn> 2 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </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> <cn type='integer'> 2 </cn> <ci> c </ci> </list> <list> <cn type='integer'> 3 </cn> <ci> e </ci> </list> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> e </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> e </ci> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> PolyGamma </ci> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> c </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <neq /> <ci> c </ci> <cn type='integer'> 1 </cn> </apply> <apply> <neq /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <gt /> <apply> <real /> <apply> <plus /> <ci> e </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 0 </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