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





http://functions.wolfram.com/07.23.03.ae18.01









  


  










Input Form





Hypergeometric2F1[-(9/4), -(9/4), 5, -z] == (4096 Sqrt[2] (2 (-576 - 7464 z - 51225 z^2 - 308100 z^3 + 6924650 z^4 - 5385404 z^5 + 495239 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 2 Sqrt[1 + z] (-576 - 7464 z - 51225 z^2 - 308100 z^3 + 6924650 z^4 - 5385404 z^5 + 495239 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-1152 - 14640 z - 98925 z^2 - 593100 z^3 + 7413850 z^4 - 4799468 z^5 + 348075 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 2 (-576 - 7464 z - 51225 z^2 - 308100 z^3 + 6924650 z^4 - 5385404 z^5 + 495239 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (13461800625 Pi z^4 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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</cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 13461800625 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </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