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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=-11/4, b>=a > For fixed z and a=-11/4, b=9/4





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









  


  








Input Form





Hypergeometric2F1[-(11/4), 9/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (-2464 - 3927 z + 5082 z^2 + 22633 z^3 + 20832 z^4 + 6144 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (-2464 - 6391 z + 1155 z^2 + 27715 z^3 + 43465 z^4 + 26976 z^5 + 6144 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-2464 - 5775 z + 2310 z^2 + 6925 z^3 + 5640 z^4 + 1536 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2464 - 3927 z + 5082 z^2 + 22633 z^3 + 20832 z^4 + 6144 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (2523675 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</apply> <apply> <times /> <cn type='integer'> 5082 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3927 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -2464 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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