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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=-17/4, b>=a > For fixed z and a=-17/4, b=-13/4





http://functions.wolfram.com/07.23.03.aa9g.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(13/4), 3/2, z] == (1/(10138590 Pi^(3/2))) ((2 (2470005 + 21329580 z + 28422462 z^2 + 6453164 z^3 + 45045 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (2470005 + 21329580 z + 28422462 z^2 + 6453164 z^3 + 45045 z^4) EllipticE[(1/2) (1 + Sqrt[z])] - (1/Sqrt[z]) ((129285 + 2470005 Sqrt[z] + 5824620 z + 21329580 z^(3/2) + 26017950 z^2 + 28422462 z^(5/2) + 23099756 z^3 + 6453164 z^(7/2) + 3648645 z^4 + 45045 z^(9/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/Sqrt[z]) ((129285 - 2470005 Sqrt[z] + 5824620 z - 21329580 z^(3/2) + 26017950 z^2 - 28422462 z^(5/2) + 23099756 z^3 - 6453164 z^(7/2) + 3648645 z^4 - 45045 z^(9/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[1/4]^2)










Standard Form





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MathML Form







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2470005 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> 129285 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </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