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





http://functions.wolfram.com/07.27.03.ab1a.01









  


  










Input Form





HypergeometricPFQ[{-(5/2), 1, 1}, {-(1/2), 7/2}, z] == (I (1920 I - 4480 I z - 304 I z^2 - 1600 I z^3 - 450 Pi^2 z^(7/2) + 900 I z^4 + 225 Pi^2 z^(9/2)))/(2048 z^2) - (15 Sqrt[1 - z] (-32 + 64 z - 12 z^2 - 20 z^3 + 15 z^4) ArcSin[Sqrt[z]])/ (512 z^(5/2)) + (1/(36864 (-1 + z)^6)) (Sqrt[1 - z] (-86032 + 236196 z - 204626 z^2 - 2752693 z^3 + 5731930 z^4 - 6090930 z^5 + 3661890 z^6 - 1185765 z^7 + 160830 z^8) Log[1 - E^(I ArcSin[Sqrt[z]])]) + (1/(36864 (-1 + z)^6)) (Sqrt[1 - z] (86032 - 236196 z + 204626 z^2 + 2752693 z^3 - 5731930 z^4 + 6090930 z^5 - 3661890 z^6 + 1185765 z^7 - 160830 z^8) Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))]) + (225/512) (-2 + z) z^(3/2) ArcSin[Sqrt[z]] Log[(1 - E^(I ArcSin[Sqrt[z]]))/(1 + E^(I ArcSin[Sqrt[z]]))] - (1/(36864 (-1 + z)^6)) (Sqrt[1 - z] (-86032 + 236196 z - 204626 z^2 - 2752693 z^3 + 5731930 z^4 - 6090930 z^5 + 3661890 z^6 - 1185765 z^7 + 160830 z^8) Log[1 + E^(I ArcSin[Sqrt[z]])]) + (225/512) I (-2 + z) z^(3/2) PolyLog[2, -E^(I ArcSin[Sqrt[z]])] - (225/512) I (-2 + z) z^(3/2) PolyLog[2, E^(I ArcSin[Sqrt[z]])]










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 450 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1600 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 304 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4480 </cn> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 1920 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2048 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 20 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 64 </cn> <ci> z </ci> </apply> <cn type='integer'> -32 </cn> </apply> <apply> <arcsin /> <apply> <power /> <ci> z 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Date Added to functions.wolfram.com (modification date)





2007-05-02