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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=-11/2





http://functions.wolfram.com/07.23.03.8972.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(11/2), 5, z] == (4 Sqrt[2] (2 (1 - z)^(1/4) (-2072576 + 63213568 z - 1166342144 z^2 + 22622102272 z^3 + 1169655023360 z^4 + 5171519370656 z^5 + 6733341773632 z^6 + 2982846462024 z^7 + 411637611528 z^8 + 11645395905 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (-2072576 + 63213568 z - 1166342144 z^2 + 22622102272 z^3 + 1169655023360 z^4 + 5171519370656 z^5 + 6733341773632 z^6 + 2982846462024 z^7 + 411637611528 z^8 + 11645395905 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(1/4) (-2072576 + 63213568 z - 1166342144 z^2 + 22622102272 z^3 + 1169655023360 z^4 + 5171519370656 z^5 + 6733341773632 z^6 + 2982846462024 z^7 + 411637611528 z^8 + 11645395905 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - Sqrt[1 - z] (-2072576 + 63213568 z - 1166342144 z^2 + 22622102272 z^3 + 1169655023360 z^4 + 5171519370656 z^5 + 6733341773632 z^6 + 2982846462024 z^7 + 411637611528 z^8 + 11645395905 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(3/4) (-2072576 + 63213568 z - 1166342144 z^2 + 22622102272 z^3 + 1169655023360 z^4 + 5171519370656 z^5 + 6733341773632 z^6 + 2982846462024 z^7 + 411637611528 z^8 + 11645395905 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (2072576 - 64249856 z + 1197754624 z^2 - 23199444224 z^3 - 147003116160 z^4 + 1686349389344 z^5 + 6515340012816 z^6 + 6322733213576 z^7 + 1969862756004 z^8 + 174554379285 z^9 + 2389770240 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]))/(2022894598725 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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<mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> <mo> &#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> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2022894598725 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <msqrt> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </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'> 23 <sep /> 4 </cn> 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Date Added to functions.wolfram.com (modification date)





2007-05-02