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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=-21/4, b>=a > For fixed z and a=-21/4, b=15/4





http://functions.wolfram.com/07.23.03.a8sc.01









  


  










Input Form





Hypergeometric2F1[-(21/4), 15/4, 4, -z] == (256 Sqrt[2] ((21216 - 66963 z + 421005 z^2 + 15270467 z^3 + 61464355 z^4 + 107544704 z^5 + 97323008 z^6 + 44892160 z^7 + 8388608 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + Sqrt[1 + z] (21216 - 66963 z + 421005 z^2 + 15270467 z^3 + 61464355 z^4 + 107544704 z^5 + 97323008 z^6 + 44892160 z^7 + 8388608 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (21216 - 72267 z + 441558 z^2 + 5607905 z^3 + 14944400 z^4 + 17501184 z^5 + 9715712 z^6 + 2097152 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (21216 - 66963 z + 421005 z^2 + 15270467 z^3 + 61464355 z^4 + 107544704 z^5 + 97323008 z^6 + 44892160 z^7 + 8388608 z^8) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1221395175 Pi z^3 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 421005 </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'> 66963 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 21216 </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> <power /> <apply> <times /> <cn type='integer'> 1221395175 </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