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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=-11/2, b>=a > For fixed z and a=-11/2, b=-7/4





http://functions.wolfram.com/07.23.03.a7y7.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(7/4), 4, z] == (2 (1 - z)^(1/4) (43008 - 852096 z + 11894400 z^2 + 282840128 z^3 + 390294560 z^4 + 49351512 z^5 - 4868864 z^6 + 512050 z^7 - 30723 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (43008 - 852096 z + 11894400 z^2 + 282840128 z^3 + 390294560 z^4 + 49351512 z^5 - 4868864 z^6 + 512050 z^7 - 30723 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-43008 + 873600 z - 12316416 z^2 + 14019904 z^3 + 416024480 z^4 + 309133288 z^5 + 1654520 z^6 - 172634 z^7 + 10241 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-43008 + 852096 z - 11894400 z^2 - 282840128 z^3 - 390294560 z^4 - 49351512 z^5 + 4868864 z^6 - 512050 z^7 + 30723 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-43008 + 852096 z - 11894400 z^2 - 282840128 z^3 - 390294560 z^4 - 49351512 z^5 + 4868864 z^6 - 512050 z^7 + 30723 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-43008 + 852096 z - 11894400 z^2 - 282840128 z^3 - 390294560 z^4 - 49351512 z^5 + 4868864 z^6 - 512050 z^7 + 30723 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (72747675 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)








Standard Form





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MathML Form







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</apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11894400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 852096 </cn> <ci> z </ci> </apply> <cn type='integer'> -43008 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 72747675 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <pi /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </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