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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=23/4, b>=a > For fixed z and a=23/4, b=23/4





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









  


  








Input Form





Hypergeometric2F1[23/4, 23/4, 1, -z] == (1/(7315 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] ((2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^10 + (2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(19/2) - (2 (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^10 - (1/(1 + z)^(21/2)) ((2727 + 40479 z - 386810 z^2 + 537566 z^3 - 162077 z^4 + 7315 z^5) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])])))








Standard Form





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MathML Form







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</apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["23", "4"], ",", FractionBox["23", "4"], ",", "1", ",", RowBox[List["-", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5021", "-", RowBox[List["65820", " ", "z"]], "+", RowBox[List["141198", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["65820", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5021", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "10"]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5021", "-", RowBox[List["65820", " ", "z"]], "+", RowBox[List["141198", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["65820", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5021", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["19", "/", "2"]]]], "-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List["5021", "-", RowBox[List["65820", " ", "z"]], "+", RowBox[List["141198", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["65820", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["5021", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "10"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["2727", "+", RowBox[List["40479", " ", "z"]], "-", RowBox[List["386810", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["537566", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["162077", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["7315", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox[RowBox[List["1", "+", "z"]]]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["21", "/", "2"]]]]]], ")"]]]], RowBox[List["7315", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "+", "z"]]]]]]]]]]]]]


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





2007-05-02