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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a=1, b>=a > For fixed z and a=1, b=2





http://functions.wolfram.com/07.23.03.3136.01









  


  








Input Form





Hypergeometric2F1[1, 2, -(9/2), z] == -((1/(630 (1 - z)^(15/2))) (Sqrt[1 - z] (-630 + z (4690 + z (-15430 + z (29994 + z (-40858 + z (63814 + 3465 z)))))) + 45045 z^(11/2) ArcSin[Sqrt[z]]))








Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3465 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 63814 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 40858 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 29994 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 15430 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 4690 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 630 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='integer'> 1 </cn> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 9 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 630 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 45045 </cn> <apply> <times /> <apply> <power /> <ci> sin </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <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 /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3465 </cn> <ci> z </ci> </apply> <cn type='integer'> 63814 </cn> </apply> </apply> <cn type='integer'> -40858 </cn> </apply> </apply> <cn type='integer'> 29994 </cn> </apply> </apply> <cn type='integer'> -15430 </cn> </apply> </apply> <cn type='integer'> 4690 </cn> </apply> </apply> <cn type='integer'> -630 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02