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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=-5/4





http://functions.wolfram.com/07.23.03.a7yl.01









  


  










Input Form





Hypergeometric2F1[-(11/2), -(5/4), 6, z] == (8 Sqrt[2] (-2 (-1441792 + 23474176 z - 193754880 z^2 + 1160614400 z^3 - 7076854400 z^4 - 133209781824 z^5 - 106107041488 z^6 - 1408300400 z^7 + 178148100 z^8 - 18928650 z^9 + 1077375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-1441792 + 23474176 z - 193754880 z^2 + 1160614400 z^3 - 7076854400 z^4 - 133209781824 z^5 - 106107041488 z^6 - 1408300400 z^7 + 178148100 z^8 - 18928650 z^9 + 1077375 z^10) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-1441792 + 23474176 z - 193754880 z^2 + 1160614400 z^3 - 7076854400 z^4 - 133209781824 z^5 - 106107041488 z^6 - 1408300400 z^7 + 178148100 z^8 - 18928650 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-1441792 + 23474176 z - 193754880 z^2 + 1160614400 z^3 - 7076854400 z^4 - 133209781824 z^5 - 106107041488 z^6 - 1408300400 z^7 + 178148100 z^8 - 18928650 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-1441792 + 23474176 z - 193754880 z^2 + 1160614400 z^3 - 7076854400 z^4 - 133209781824 z^5 - 106107041488 z^6 - 1408300400 z^7 + 178148100 z^8 - 18928650 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (1441792 - 22753280 z + 182603520 z^2 - 1072755200 z^3 + 6567299200 z^4 + 51933559104 z^5 + 25758787600 z^6 - 1277291600 z^7 + 163694700 z^8 - 18066750 z^9 + 1077375 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (337621959675 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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</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'> 5 <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> </apply> </apply> <cn 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type='integer'> 22753280 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 1441792 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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 /> 4 </cn> </apply> <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='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 337621959675 </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>










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Date Added to functions.wolfram.com (modification date)





2007-05-02