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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=-9/4





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









  


  










Input Form





Hypergeometric2F1[-(17/4), -(9/4), -(3/2), z] == (1/(336 Pi^(3/2))) ((2 (84 - 525 z + 2114 z^2 + 435 z^3 - 60 z^4) EllipticE[(1/2) (1 - Sqrt[z])] + 2 (84 - 525 z + 2114 z^2 + 435 z^3 - 60 z^4) EllipticE[(1/2) (1 + Sqrt[z])] + (-84 - 42 Sqrt[z] + 525 z + 259 z^(3/2) - 2114 z^2 - 2280 z^(5/2) - 435 z^3 + 15 z^(7/2) + 60 z^4) EllipticK[(1/2) (1 - Sqrt[z])] + (-84 + 42 Sqrt[z] + 525 z - 259 z^(3/2) - 2114 z^2 + 2280 z^(5/2) - 435 z^3 - 15 z^(7/2) + 60 z^4) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[1/4]^2)










Standard Form





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MathML Form







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type='integer'> -84 </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> <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