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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=-1/2, a2>=-1/2 > For fixed z and a1=-1/2, a2=1, a3>=1 > For fixed z and a1=-1/2, a2=1, a3=4 > For fixed z and a1=-1/2, a2=1, a3=4, b1=5/2





http://functions.wolfram.com/07.27.03.akgo.01









  


  










Input Form





HypergeometricPFQ[{-(1/2), 1, 4}, {5/2, 5/2}, z] == -((3 I (24 Pi^2 + 296 I Sqrt[z] - 120 Pi^2 z + 420 I z^(3/2) + 105 Pi^2 z^2))/(4096 z^(3/2))) + (15 Sqrt[1 - z] (-10 + 21 z) ArcSin[Sqrt[z]])/(1024 z^(3/2)) + (1/(25600 (-1 + z)^5 z)) (3 Sqrt[1 - z] (600 - 13792 z + 37289 z^2 - 48967 z^3 + 33400 z^4 - 11165 z^5 + 1375 z^6) Log[1 - E^(I ArcSin[Sqrt[z]])]) - (1/(25600 (-1 + z)^5 z)) (3 Sqrt[1 - z] (600 - 13792 z + 37289 z^2 - 48967 z^3 + 33400 z^4 - 11165 z^5 + 1375 z^6) Log[(1 - E^(I ArcSin[Sqrt[z]]))/ (1 + E^(I ArcSin[Sqrt[z]]))]) - (9 (8 - 40 z + 35 z^2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))])/ (1024 z^(3/2)) - (1/(25600 (-1 + z)^5 z)) (3 Sqrt[1 - z] (600 - 13792 z + 37289 z^2 - 48967 z^3 + 33400 z^4 - 11165 z^5 + 1375 z^6) Log[1 + E^(I ArcSin[Sqrt[z]])]) - (9 I (8 - 40 z + 35 z^2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])])/ (1024 z^(3/2)) + (9 I (8 - 40 z + 35 z^2) PolyLog[2, E^(I ArcSin[Sqrt[z]])])/(1024 z^(3/2))










Standard Form





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MathML Form







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type='integer'> 9 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> 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/> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <arcsin /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1024 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> 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Date Added to functions.wolfram.com (modification date)





2007-05-02