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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=17/4





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









  


  








Input Form





Hypergeometric2F1[-(15/4), 17/4, 3, -z] == (64 Sqrt[2] (2 Sqrt[1 + z] (-770 + 10395 z + 500576 z^2 + 1881856 z^3 + 2310144 z^4 + 917504 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 2 (-770 + 9625 z + 510971 z^2 + 2382432 z^3 + 4192000 z^4 + 3227648 z^5 + 917504 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (-1540 + 19635 z + 401707 z^2 + 1206656 z^3 + 1284096 z^4 + 458752 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (-770 + 10395 z + 500576 z^2 + 1881856 z^3 + 2310144 z^4 + 917504 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (19684665 Pi z^2 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 500576 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10395 </cn> <ci> z </ci> </apply> <cn type='integer'> -770 </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