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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=21/4





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









  


  








Input Form





Hypergeometric2F1[-(11/4), 21/4, 4, -z] == (256 Sqrt[2] (Sqrt[1 + z] (2464 - 17325 z + 133056 z^2 + 3990016 z^3 + 9338880 z^4 + 5505024 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (2464 - 14861 z + 115731 z^2 + 4123072 z^3 + 13328896 z^4 + 14843904 z^5 + 5505024 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2464 - 15477 z + 119889 z^2 + 1476736 z^3 + 2721792 z^4 + 1376256 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (2464 - 17325 z + 133056 z^2 + 3990016 z^3 + 9338880 z^4 + 5505024 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (334639305 Pi z^3 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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</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> <power /> <apply> <times /> <cn type='integer'> 334639305 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02