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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3},{b1,b2},z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a1=-7/2, a2>=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3>=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3=-7/2 > For fixed z and a1=-7/2, a2=-7/2, a3=-7/2, b1=1/2





http://functions.wolfram.com/07.27.03.1024.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {1/2, 1/2}, z] == (1225 (35 Pi^2 Sqrt[-z] + 630 Pi^2 (-z)^(3/2) + 504 Pi^2 (-z)^(5/2) + 16 Pi^2 (-z)^(7/2)))/49152 + (Sqrt[1 - z] (147456 - 20970351 z + 52409444 z^2 - 4998764 z^3))/147456 - (1/49152) (35 (-25725 Sqrt[-z] + 22050 (-z)^(3/2) + 324576 (-z)^(5/2) + 23584 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]]) - (1225 (35 Sqrt[-z] + 630 (-z)^(3/2) + 504 (-z)^(5/2) + 16 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/8192 + (1/4096) (1225 (35 Sqrt[-z] + 630 (-z)^(3/2) + 504 (-z)^(5/2) + 16 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) + (1/4096) (1225 (35 Sqrt[-z] + 630 (-z)^(3/2) + 504 (-z)^(5/2) + 16 (-z)^(7/2)) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]]) - (1/4096) (1225 (35 Sqrt[-z] + 630 (-z)^(3/2) + 504 (-z)^(5/2) + 16 (-z)^(7/2)) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])










Standard Form





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MathML Form







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</mi> </mrow> </msqrt> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> Li </mi> <annotation-xml encoding='MathML-Content'> <ci> PolyLog </ci> </annotation-xml> </semantics> <mn> 2 </mn> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> - </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 4096 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1225 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 504 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 630 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ln /> <apply> <plus /> <apply> 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type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1225 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 504 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 630 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <plus 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Date Added to functions.wolfram.com (modification date)





2007-05-02