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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.aa9a.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(13/4), -(5/2), z] == (1/(480 Pi^(3/2))) ((-2 (-120 + 648 z - 1541 z^2 + 2866 z^3 + 195 z^4) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-120 + 648 z - 1541 z^2 + 2866 z^3 + 195 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (-120 - 60 Sqrt[z] + 648 z + 319 z^(3/2) - 1541 z^2 - 746 z^(5/2) + 2866 z^3 + 2535 z^(7/2) + 195 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (-120 + 60 Sqrt[z] + 648 z - 319 z^(3/2) - 1541 z^2 + 746 z^(5/2) + 2866 z^3 - 2535 z^(7/2) + 195 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)










Standard Form





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MathML Form







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</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> <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