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





http://functions.wolfram.com/07.27.03.2648.01









  


  








Input Form





HypergeometricPFQ[{-(7/2), -(5/2), 1/2}, {5/2, 7/2}, z] == (525 Pi^2 (-1 - 20 z))/(524288 (-z)^(3/2)) + (Sqrt[1 - z] (-315 - 55230 z + 1202104 z^2 + 544576 z^3 + 66496 z^4 + 384 z^5))/(2097152 z^2) - (105 (-3 - 284 z - 3400 z^2 - 9600 z^3 - 3200 z^4 - 256 z^5) Log[Sqrt[1 - z] + Sqrt[-z]])/(2097152 (-z)^(5/2)) - (1575 (-1 - 20 z) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(262144 (-z)^(3/2)) + (1575 (-1 - 20 z) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/(131072 (-z)^(3/2)) + (1575 (-1 - 20 z) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (131072 (-z)^(3/2)) - (1575 (-1 - 20 z) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (131072 (-z)^(3/2))








Standard Form





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MathML Form







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</cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9600 </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'> 3400 </cn> <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'> 284 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -3 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <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> <times /> <cn type='integer'> 2097152 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1575 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -20 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ln /> <apply> <plus /> <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> 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3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1202104 </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'> 55230 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -315 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2097152 </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'> 1575 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -20 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </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 /> <apply> <times /> <cn type='integer'> 131072 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1575 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -20 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </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> 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Rule Form





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





2007-05-02