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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=-21/4, b>=a > For fixed z and a=-21/4, b=3/2





http://functions.wolfram.com/07.23.03.a8l9.01









  


  








Input Form





Hypergeometric2F1[-(21/4), 3/2, 6, z] == (1024 Sqrt[2] (-2 (2036736 - 18012384 z + 68239938 z^2 - 137403435 z^3 + 116953200 z^4 - 458276288 z^5 + 526660112 z^6 - 360983184 z^7 + 153379160 z^8 - 37452800 z^9 + 4037880 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (2036736 - 18012384 z + 68239938 z^2 - 137403435 z^3 + 116953200 z^4 - 458276288 z^5 + 526660112 z^6 - 360983184 z^7 + 153379160 z^8 - 37452800 z^9 + 4037880 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-2036736 + 16994016 z - 60061170 z^2 + 109869045 z^3 - 70171920 z^4 + 107416688 z^5 - 87006208 z^6 + 41985360 z^7 - 11394680 z^8 + 1345960 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (2036736 - 18012384 z + 68239938 z^2 - 137403435 z^3 + 116953200 z^4 - 458276288 z^5 + 526660112 z^6 - 360983184 z^7 + 153379160 z^8 - 37452800 z^9 + 4037880 z^10) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (2036736 - 18012384 z + 68239938 z^2 - 137403435 z^3 + 116953200 z^4 - 458276288 z^5 + 526660112 z^6 - 360983184 z^7 + 153379160 z^8 - 37452800 z^9 + 4037880 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (2036736 - 18012384 z + 68239938 z^2 - 137403435 z^3 + 116953200 z^4 - 458276288 z^5 + 526660112 z^6 - 360983184 z^7 + 153379160 z^8 - 37452800 z^9 + 4037880 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (168441498225 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4037880 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 37452800 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 153379160 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 360983184 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 526660112 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 458276288 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 116953200 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 137403435 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> 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</cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 168441498225 </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'> 5 </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