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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/07.23.03.8973.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(11/2), 6, z] == (8 Sqrt[2] (2 (1 - z)^(1/4) (33161216 - 923332608 z + 14103167232 z^2 - 173876043264 z^3 + 2538332759424 z^4 + 101232212714304 z^5 + 372235058844208 z^6 + 415433534769648 z^7 + 161092871715204 z^8 + 19766075435106 z^9 + 503141794155 z^10) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (33161216 - 923332608 z + 14103167232 z^2 - 173876043264 z^3 + 2538332759424 z^4 + 101232212714304 z^5 + 372235058844208 z^6 + 415433534769648 z^7 + 161092871715204 z^8 + 19766075435106 z^9 + 503141794155 z^10) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (33161216 - 923332608 z + 14103167232 z^2 - 173876043264 z^3 + 2538332759424 z^4 + 101232212714304 z^5 + 372235058844208 z^6 + 415433534769648 z^7 + 161092871715204 z^8 + 19766075435106 z^9 + 503141794155 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (33161216 - 923332608 z + 14103167232 z^2 - 173876043264 z^3 + 2538332759424 z^4 + 101232212714304 z^5 + 372235058844208 z^6 + 415433534769648 z^7 + 161092871715204 z^8 + 19766075435106 z^9 + 503141794155 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (33161216 - 923332608 z + 14103167232 z^2 - 173876043264 z^3 + 2538332759424 z^4 + 101232212714304 z^5 + 372235058844208 z^6 + 415433534769648 z^7 + 161092871715204 z^8 + 19766075435106 z^9 + 503141794155 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-33161216 + 939913216 z - 14561724672 z^2 + 180842618880 z^3 - 2623990900608 z^4 - 8645021845824 z^5 + 148599219826064 z^6 + 451190281404272 z^7 + 373546743723660 z^8 + 102209663222238 z^9 + 8096111558535 z^10 + 100370350080 z^11) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (365334764529735 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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<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> 365334764529735 </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> 5 </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> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 8 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Date Added to functions.wolfram.com (modification date)





2007-05-02