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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=-23/4, b>=a > For fixed z and a=-23/4, b=-11/4





http://functions.wolfram.com/07.23.03.9205.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(11/4), 3, -z] == (64 Sqrt[2] ((-Sqrt[1 + z]) (7084 + 256795 z - 12315537 z^2 + 37328270 z^3 - 20592982 z^4 + 850311 z^5 + 53515 z^6 + 2464 z^7) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (7084 + 263879 z - 12058742 z^2 + 25012733 z^3 + 16735288 z^4 - 19742671 z^5 + 903826 z^6 + 55979 z^7 + 2464 z^8) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 4 (1771 + 65527 z + 269634 z^2 - 10171624 z^3 + 18990263 z^4 - 6271881 z^5 + 3388 z^6 + 154 z^7) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + Sqrt[1 + z] (7084 + 256795 z - 12315537 z^2 + 37328270 z^3 - 20592982 z^4 + 850311 z^5 + 53515 z^6 + 2464 z^7) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (422463195 Pi z^2 Sqrt[1 + Sqrt[1 + z]])










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 256795 </cn> <ci> z </ci> </apply> <cn type='integer'> 7084 </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> <power /> <apply> <times /> <cn type='integer'> 422463195 </cn> <pi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </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