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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=1/4





http://functions.wolfram.com/07.23.03.a7zo.01









  


  










Input Form





Hypergeometric2F1[-(11/2), 1/4, 5, z] == (4 Sqrt[2] (-2 (1 - z)^(1/4) (24576 - 282624 z + 1602048 z^2 - 6888960 z^3 - 17643520 z^4 + 8015264 z^5 - 3554976 z^6 + 1155352 z^7 - 234080 z^8 + 21945 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (24576 - 282624 z + 1602048 z^2 - 6888960 z^3 - 17643520 z^4 + 8015264 z^5 - 3554976 z^6 + 1155352 z^7 - 234080 z^8 + 21945 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (24576 - 294912 z + 1741056 z^2 - 7664640 z^3 + 22037120 z^4 + 2866144 z^5 - 1251568 z^6 + 399304 z^7 - 79420 z^8 + 7315 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (24576 - 282624 z + 1602048 z^2 - 6888960 z^3 - 17643520 z^4 + 8015264 z^5 - 3554976 z^6 + 1155352 z^7 - 234080 z^8 + 21945 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (24576 - 282624 z + 1602048 z^2 - 6888960 z^3 - 17643520 z^4 + 8015264 z^5 - 3554976 z^6 + 1155352 z^7 - 234080 z^8 + 21945 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (24576 - 282624 z + 1602048 z^2 - 6888960 z^3 - 17643520 z^4 + 8015264 z^5 - 3554976 z^6 + 1155352 z^7 - 234080 z^8 + 21945 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (72747675 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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&#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </list> <list> <cn type='integer'> 5 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 72747675 </cn> <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> 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<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> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02