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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=-15/4, b>=a > For fixed z and a=-15/4, b=-15/4





http://functions.wolfram.com/07.23.03.ab14.01









  


  










Input Form





Hypergeometric2F1[-(15/4), -(15/4), 4, -z] == (256 Sqrt[2] ((-Sqrt[1 + z]) (12320 + 273735 z + 4487175 z^2 - 115440602 z^3 + 230653998 z^4 - 94793373 z^5 + 6362747 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (12320 + 286055 z + 4760910 z^2 - 110953427 z^3 + 115213396 z^4 + 135860625 z^5 - 88430626 z^6 + 6362747 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (12320 + 273735 z + 4487175 z^2 - 115440602 z^3 + 230653998 z^4 - 94793373 z^5 + 6362747 z^6) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (12320 + 282975 z + 4691610 z^2 + 27484873 z^3 - 338216916 z^4 + 424019169 z^5 - 113110342 z^6 + 4542615 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (17866104795 Pi z^3 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 17866104795 </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