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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 8 and fixed z and a>0 > For fixed z and a=7/8, b>=a > For fixed z and a=7/8, b=35/8





http://functions.wolfram.com/07.23.03.c19y.01









  


  








Input Form





Hypergeometric2F1[7/8, 35/8, 2, z] == (16 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-209 + 885 z - 936 z^2 + 320 z^3) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (209 (1 + Sqrt[1 - z] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) - 3 (86 + 295 Sqrt[1 - z] + 295 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z + 3 (83 + 312 Sqrt[1 - z] + 312 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^2 - 80 (1 + 4 Sqrt[1 - z] + 4 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z]) z^3) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (5643 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(13/4) z)








Standard Form





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MathML Form







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z </ci> </apply> </apply> <cn type='rational'> 13 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "8"], ",", FractionBox["35", "8"], ",", "2", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["16", " ", SuperscriptBox["2", RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "209"]], "+", RowBox[List["885", " ", "z"]], "-", RowBox[List["936", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["320", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["209", " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]]]], "-", RowBox[List["3", " ", RowBox[List["(", RowBox[List["86", "+", RowBox[List["295", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["295", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", "z"]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["83", "+", RowBox[List["312", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["312", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["80", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["4", " ", SqrtBox[RowBox[List["1", "-", "z"]]]]], "+", RowBox[List["4", " ", SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]], ")"]], " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SqrtBox[RowBox[List["1", "-", "z"]]], RowBox[List[SqrtBox["2"], " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]], "-", "z"]]]]]]]], "]"]]]]]], ")"]]]], RowBox[List["5643", " ", "\[Pi]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["13", "/", "4"]]], " ", "z"]]]]]]]


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





2007-05-02