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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=7/4, b>=a > For fixed z and a=7/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[7/4, 19/4, 7/2, z] == (1/(693 Pi^(3/2) z^(5/2))) (2 ((2 Sqrt[z] (-10 + 15 z - 69 z^2 + 32 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3 + (2 Sqrt[z] (-10 + 15 z - 69 z^2 + 32 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/ (-1 + z)^3 - ((20 - 30 Sqrt[z] - 15 z + 30 z^(3/2) - 45 z^2 - 24 z^(5/2) + 32 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/ ((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2) - ((20 + 30 Sqrt[z] - 15 z - 30 z^(3/2) - 45 z^2 + 24 z^(5/2) + 32 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) Gamma[1/4]^2)










Standard Form





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MathML Form







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<cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["7", "4"], ",", FractionBox["19", "4"], ",", FractionBox["7", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10"]], "+", RowBox[List["15", " ", "z"]], "-", RowBox[List["69", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "10"]], "+", RowBox[List["15", " ", "z"]], "-", RowBox[List["69", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "3"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["20", "-", RowBox[List["30", " ", SqrtBox["z"]]], "-", RowBox[List["15", " ", "z"]], "+", RowBox[List["30", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["45", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["20", "+", RowBox[List["30", " ", SqrtBox["z"]]], "-", RowBox[List["15", " ", "z"]], "-", RowBox[List["30", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["45", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["24", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["32", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["693", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]]]]










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





2007-05-02