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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/07.27.03.1025.01









  


  








Input Form





HypergeometricPFQ[{-(7/2), -(7/2), -(7/2)}, {1/2, 3/2}, z] == (1225 (35 Pi^2 Sqrt[-z] + 315 Pi^2 (-z)^(3/2) + 168 Pi^2 (-z)^(5/2) + 4 Pi^2 (-z)^(7/2)))/98304 + (Sqrt[1 - z] (18488493 - 847540770 z + 1259760536 z^2 - 85109264 z^3))/ 18874368 - (35 (-3675 + 1176000 z + 2822400 z^2 - 7676928 z^3 + 390784 z^4) Log[Sqrt[1 - z] + Sqrt[-z]])/(6291456 Sqrt[-z]) - (1225 (35 Sqrt[-z] + 315 (-z)^(3/2) + 168 (-z)^(5/2) + 4 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]]^2)/16384 + (1/8192) (1225 (35 Sqrt[-z] + 315 (-z)^(3/2) + 168 (-z)^(5/2) + 4 (-z)^(7/2)) Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]]) + (1225 (35 Sqrt[-z] + 315 (-z)^(3/2) + 168 (-z)^(5/2) + 4 (-z)^(7/2)) PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/8192 - (1/8192) (1225 (35 Sqrt[-z] + 315 (-z)^(3/2) + 168 (-z)^(5/2) + 4 (-z)^(7/2)) PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])








Standard Form





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MathML Form







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<ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 16384 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 390784 </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'> 7676928 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2822400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1176000 </cn> <ci> z </ci> </apply> <cn type='integer'> -3675 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> 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</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> </apply> <apply> <times /> <cn type='integer'> 1225 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <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'> 168 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <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'> 315 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z 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Rule Form





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





2007-05-02