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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=-3/2





http://functions.wolfram.com/07.23.03.a98e.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(3/2), 6, z] == (128 Sqrt[2] (2 (1 - z)^(1/4) (155648 - 2407680 z + 18893296 z^2 - 108130064 z^3 + 640355100 z^4 + 6338123582 z^5 + 3978265935 z^6 + 78234624 z^7 - 6030336 z^8 + 299520 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (155648 - 2407680 z + 18893296 z^2 - 108130064 z^3 + 640355100 z^4 + 6338123582 z^5 + 3978265935 z^6 + 78234624 z^7 - 6030336 z^8 + 299520 z^9) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (155648 - 2407680 z + 18893296 z^2 - 108130064 z^3 + 640355100 z^4 + 6338123582 z^5 + 3978265935 z^6 + 78234624 z^7 - 6030336 z^8 + 299520 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (155648 - 2407680 z + 18893296 z^2 - 108130064 z^3 + 640355100 z^4 + 6338123582 z^5 + 3978265935 z^6 + 78234624 z^7 - 6030336 z^8 + 299520 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (155648 - 2407680 z + 18893296 z^2 - 108130064 z^3 + 640355100 z^4 + 6338123582 z^5 + 3978265935 z^6 + 78234624 z^7 - 6030336 z^8 + 299520 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (155648 - 2485504 z + 20082544 z^2 - 117358288 z^3 + 692757100 z^4 - 1781701978 z^5 - 7543304251 z^6 - 2279506944 z^7 + 79392768 z^8 - 6090240 z^9 + 299520 z^10) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (499773959685 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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</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> 499773959685 </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'> 19 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </list> <list> <cn type='integer'> 6 </cn> </list> <ci> z </ci> </apply> 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</apply> <apply> <times /> <cn type='integer'> 6338123582 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 640355100 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 108130064 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 18893296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2407680 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 155648 </cn> </apply> <apply> <ci> EllipticE </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> 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Date Added to functions.wolfram.com (modification date)





2007-05-02