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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=3/2





http://functions.wolfram.com/07.27.03.2642.01









  


  








Input Form





HypergeometricPFQ[{-(7/2), -(5/2), 1/2}, {3/2, 5/2}, z] == (175 Pi^2)/(16384 Sqrt[-z]) - (Sqrt[1 - z] (315 - 134448 z - 137812 z^2 - 30272 z^3 - 288 z^4))/ (196608 z) - (35 (3 + 350 z + 1440 z^2 + 960 z^3 + 128 z^4) Log[Sqrt[1 - z] + Sqrt[-z]])/(65536 (-z)^(3/2)) - (525 Log[Sqrt[1 - z] + Sqrt[-z]]^2)/(8192 Sqrt[-z]) + (525 Log[Sqrt[1 - z] + Sqrt[-z]] Log[1 + Sqrt[1 - z] + Sqrt[-z]])/ (4096 Sqrt[-z]) + (525 PolyLog[2, -Sqrt[1 - z] - Sqrt[-z]])/ (4096 Sqrt[-z]) - (525 PolyLog[2, 1 - Sqrt[1 - z] - Sqrt[-z]])/ (4096 Sqrt[-z])








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 525 </cn> <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> </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'> 4096 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 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<ci> z </ci> </apply> </apply> <cn type='integer'> 315 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 196608 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 525 </cn> <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'> 4096 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> 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type='integer'> 175 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 16384 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02