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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=-9/2, b>=a > For fixed z and a=-9/2, b=-11/4





http://functions.wolfram.com/07.23.03.a9z9.01









  


  








Input Form





Hypergeometric2F1[-(9/2), -(11/4), 6, z] == (16 Sqrt[2] (-2 (1 - z)^(1/4) (-458752 + 8271872 z - 77691264 z^2 + 552065920 z^3 - 4280325056 z^4 - 67327810848 z^5 - 85304981112 z^6 - 21696542016 z^7 - 531990690 z^8 + 9388071 z^9) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-458752 + 8271872 z - 77691264 z^2 + 552065920 z^3 - 4280325056 z^4 - 67327810848 z^5 - 85304981112 z^6 - 21696542016 z^7 - 531990690 z^8 + 9388071 z^9) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-458752 + 8501248 z - 81784192 z^2 + 590157568 z^3 - 4549448512 z^4 + 8677456672 z^5 + 91943798472 z^6 + 71917185912 z^7 + 10141536102 z^8 + 3129357 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1 - z)^(1/4) (-458752 + 8271872 z - 77691264 z^2 + 552065920 z^3 - 4280325056 z^4 - 67327810848 z^5 - 85304981112 z^6 - 21696542016 z^7 - 531990690 z^8 + 9388071 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-458752 + 8271872 z - 77691264 z^2 + 552065920 z^3 - 4280325056 z^4 - 67327810848 z^5 - 85304981112 z^6 - 21696542016 z^7 - 531990690 z^8 + 9388071 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-458752 + 8271872 z - 77691264 z^2 + 552065920 z^3 - 4280325056 z^4 - 67327810848 z^5 - 85304981112 z^6 - 21696542016 z^7 - 531990690 z^8 + 9388071 z^9) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (591307651935 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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&#8290; </mo> <mrow> <mi> K </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <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> <mo> + </mo> <mrow> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9388071 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 531990690 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 21696542016 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> 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</cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 67327810848 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4280325056 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 552065920 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 77691264 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8271872 </cn> <ci> z </ci> </apply> <cn type='integer'> -458752 </cn> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn 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Date Added to functions.wolfram.com (modification date)





2007-05-02