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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=-11/2, b>=a > For fixed z and a=-11/2, b=-21/4





http://functions.wolfram.com/07.23.03.a7w9.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(21/4), 6, z] == (8 Sqrt[2] (2 (131072 - 3510272 z + 51217664 z^2 - 597414400 z^3 + 8133566336 z^4 + 497785503424 z^5 + 1926229630576 z^6 + 2197751175568 z^7 + 859834067060 z^8 + 105303309102 z^9 + 2633313715 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (131072 - 3510272 z + 51217664 z^2 - 597414400 z^3 + 8133566336 z^4 + 497785503424 z^5 + 1926229630576 z^6 + 2197751175568 z^7 + 859834067060 z^8 + 105303309102 z^9 + 2633313715 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (131072 - 3444736 z + 49515776 z^2 - 573184512 z^3 + 7854448000 z^4 + 234927838144 z^5 + 728051758128 z^6 + 671755274192 z^7 + 205401607556 z^8 + 17999991670 z^9 + 243061325 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (131072 - 3510272 z + 51217664 z^2 - 597414400 z^3 + 8133566336 z^4 + 497785503424 z^5 + 1926229630576 z^6 + 2197751175568 z^7 + 859834067060 z^8 + 105303309102 z^9 + 2633313715 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (131072 - 3510272 z + 51217664 z^2 - 597414400 z^3 + 8133566336 z^4 + 497785503424 z^5 + 1926229630576 z^6 + 2197751175568 z^7 + 859834067060 z^8 + 105303309102 z^9 + 2633313715 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (131072 - 3510272 z + 51217664 z^2 - 597414400 z^3 + 8133566336 z^4 + 497785503424 z^5 + 1926229630576 z^6 + 2197751175568 z^7 + 859834067060 z^8 + 105303309102 z^9 + 2633313715 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1066796155425 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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<mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mfrac> <mroot> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 4 </mn> </mroot> <mrow> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2633313715 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 105303309102 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 859834067060 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2197751175568 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1926229630576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 497785503424 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 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&#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'> 11 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 21 <sep /> 4 </cn> </apply> </list> <list> <cn type='integer'> 6 </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> 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Date Added to functions.wolfram.com (modification date)





2007-05-02