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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=-11/4





http://functions.wolfram.com/07.23.03.a7xm.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(11/4), 6, z] == (8 Sqrt[2] (2 (1 - z)^(1/4) (1441792 - 28790784 z + 302835456 z^2 - 2442947584 z^3 + 21856872576 z^4 + 422773935552 z^5 + 672461172624 z^6 + 229280819184 z^7 + 8728223724 z^8 - 306676986 z^9 + 9388071 z^10) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (1441792 - 28790784 z + 302835456 z^2 - 2442947584 z^3 + 21856872576 z^4 + 422773935552 z^5 + 672461172624 z^6 + 229280819184 z^7 + 8728223724 z^8 - 306676986 z^9 + 9388071 z^10) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1441792 - 29511680 z + 317095680 z^2 - 2591733760 z^3 + 23051262080 z^4 - 31419580224 z^5 - 603374748720 z^6 - 617585848080 z^7 - 120904958340 z^8 - 102821730 z^9 + 3129357 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (1441792 - 28790784 z + 302835456 z^2 - 2442947584 z^3 + 21856872576 z^4 + 422773935552 z^5 + 672461172624 z^6 + 229280819184 z^7 + 8728223724 z^8 - 306676986 z^9 + 9388071 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (1441792 - 28790784 z + 302835456 z^2 - 2442947584 z^3 + 21856872576 z^4 + 422773935552 z^5 + 672461172624 z^6 + 229280819184 z^7 + 8728223724 z^8 - 306676986 z^9 + 9388071 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (1441792 - 28790784 z + 302835456 z^2 - 2442947584 z^3 + 21856872576 z^4 + 422773935552 z^5 + 672461172624 z^6 + 229280819184 z^7 + 8728223724 z^8 - 306676986 z^9 + 9388071 z^10) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (1773922955805 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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<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> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9388071 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 306676986 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8728223724 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 229280819184 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 672461172624 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 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<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> 10 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 306676986 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8728223724 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 229280819184 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 672461172624 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 422773935552 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 21856872576 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - 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Date Added to functions.wolfram.com (modification date)





2007-05-02