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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions and 2F1with algebraic arguments





http://functions.wolfram.com/07.24.26.0205.01









  


  








Input Form





(Sqrt[z] + Sqrt[1 + z])^(1 - c) Hypergeometric2F1Regularized[a, 1/2 + a, c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] Hypergeometric2F1[1 + a - c, 3/2 + a - c, 3/2 + 2 a - c, (Sqrt[z] - Sqrt[1 + z])/(2 Sqrt[z])] == ((2^(-(1/2) + 4 a - c) Gamma[3/2 + 2 a - c])/(Pi Gamma[2 a])) MeijerG[{{(3 - c)/2}, {2 - (3 c)/2 + 2 a, 1 - c/2 + 2 a, (1 + c)/2}}, {{(1 - c)/2 + a, (3 - 2 c)/4 + a, 1 - c/2 + a, (5 - 2 c)/4 + a}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





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MathML Form







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</mo> <mi> c </mi> </mrow> </mrow> <mn> 4 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;4&quot;]], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;1&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List[&quot;3&quot;, &quot;-&quot;, &quot;c&quot;]], &quot;2&quot;], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;a&quot;]], &quot;-&quot;, FractionBox[RowBox[List[&quot;3&quot;, &quot; &quot;, &quot;c&quot;]], &quot;2&quot;], &quot;+&quot;, &quot;2&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;2&quot;, &quot; 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</mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29