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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=-1/2, a2>=-1/2 > For fixed z and a1=-1/2, a2=1/2, a3>=1/2 > For fixed z and a1=-1/2, a2=1/2, a3=1/2 > For fixed z and a1=-1/2, a2=1/2, a3=1/2, b1=4





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









  


  








Input Form





HypergeometricPFQ[{-(1/2), 1/2, 1/2}, {4, 4}, z] == (2048 (-1118 - 8356 z - 8388 z^2 + 75 z^3) EllipticE[1/2 - Sqrt[1 - z]/2]^2)/ (91875 Pi^2 z^3) + (2048 Sqrt[1 - z] (838 + 5433 z + 4735 z^2) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (91875 Pi^2 z^3) - (2048 (-1118 - 8356 z - 8388 z^2 + 75 z^3) EllipticE[1/2 - Sqrt[1 - z]/2] EllipticK[1/2 - Sqrt[1 - z]/2])/ (91875 Pi^2 z^3) - (1024 Sqrt[1 - z] (838 + 5433 z + 4735 z^2) EllipticK[1/2 - Sqrt[1 - z]/2]^2)/(91875 Pi^2 z^3) + (1024 (-838 - 5084 z - 2734 z^2 + 1875 z^3) EllipticK[1/2 - Sqrt[1 - z]/2]^ 2)/(91875 Pi^2 z^3)








Standard Form





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MathML Form







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<msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='integer'> 4 </cn> <cn type='integer'> 4 </cn> </list> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2048 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 75 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8388 </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'> 8356 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1118 </cn> 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type='integer'> -1118 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn 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5084 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -838 </cn> </apply> <apply> <power /> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <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> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 91875 </cn> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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