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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=-19/4, b>=a > For fixed z and a=-19/4, b=-9/2





http://functions.wolfram.com/07.23.03.a90y.01









  


  










Input Form





Hypergeometric2F1[-(19/4), -(9/2), 5, z] == (8 Sqrt[2] (2 (1 - z)^(1/4) (-233472 + 5700608 z - 81996096 z^2 + 1199936640 z^3 + 41647040800 z^4 + 119146482432 z^5 + 89395836732 z^6 + 18485559216 z^7 + 728927865 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-233472 + 5700608 z - 81996096 z^2 + 1199936640 z^3 + 41647040800 z^4 + 119146482432 z^5 + 89395836732 z^6 + 18485559216 z^7 + 728927865 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-233472 + 5700608 z - 81996096 z^2 + 1199936640 z^3 + 41647040800 z^4 + 119146482432 z^5 + 89395836732 z^6 + 18485559216 z^7 + 728927865 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-233472 + 5700608 z - 81996096 z^2 + 1199936640 z^3 + 41647040800 z^4 + 119146482432 z^5 + 89395836732 z^6 + 18485559216 z^7 + 728927865 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-233472 + 5700608 z - 81996096 z^2 + 1199936640 z^3 + 41647040800 z^4 + 119146482432 z^5 + 89395836732 z^6 + 18485559216 z^7 + 728927865 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (233472 - 5817344 z + 84824512 z^2 - 1240411200 z^3 - 2152680160 z^4 + 63228403328 z^5 + 133572406764 z^6 + 68104381068 z^7 + 8772975405 z^8 + 162938880 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]))/(155607276825 Pi Sqrt[1 + Sqrt[1 - z]] z^4)










Standard Form





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MathML Form







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</mi> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 162938880 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8772975405 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 68104381068 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 133572406764 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 63228403328 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2152680160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 1240411200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 84824512 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5817344 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</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'> 19 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </list> <list> <cn type='integer'> 5 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <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'> 3 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 728927865 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn 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</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> <power /> <apply> <times /> <cn type='integer'> 155607276825 </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> </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'> 4 </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