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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=-5/2 > For fixed z and a1=-7/2, a2=-7/2, a3=-5/2, b1=-1/2





http://functions.wolfram.com/07.27.03.1098.01









  


  










Input Form





HypergeometricPFQ[{-(7/2), -(7/2), -(5/2)}, {-(1/2), 7/2}, z] == -((3675 (-z)^(3/2) (25 Pi^2 - 8 Pi^2 z))/65536) + (1/(16777216 z^2)) (Sqrt[1 - z] (-735 + 28910 z + 15326424 z^2 + 253985232 z^3 - 314308096 z^4 + 3925760 z^5)) + (1/(16777216 (-z)^(5/2))) (105 (7 - 280 z + 14000 z^2 + 448000 z^3 + 1008000 z^4 - 1870848 z^5 + 10240 z^6) Log[Sqrt[1 - z] + Sqrt[-z]]) + (11025 (25 - 8 z) (-z)^(3/2) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/32768 - (11025 (25 - 8 z) (-z)^(3/2) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/16384 - (11025 (25 - 8 z) (-z)^(3/2) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/16384 + (11025 (25 - 8 z) (-z)^(3/2) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/16384










Standard Form





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MathML Form







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<times /> <cn type='integer'> 25 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 65536 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <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'> 3925760 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 314308096 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 253985232 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15326424 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 28910 </cn> <ci> z </ci> </apply> <cn type='integer'> -735 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 16777216 </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'> 11025 </cn> <apply> <plus /> <cn type='integer'> 25 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </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> <apply> <times /> <cn type='integer'> -1 </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> <apply> <power /> <cn type='integer'> 16384 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11025 </cn> <apply> <plus /> <cn type='integer'> 25 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <ci> PolyLog </ci> <cn type='integer'> 2 </cn> <apply> <plus /> 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Rule Form





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





2007-05-02