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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=15/4, b>=a > For fixed z and a=15/4, b=19/4





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









  


  










Input Form





Hypergeometric2F1[15/4, 19/4, 5/2, z] == (1/(17787 Pi^(3/2) z^(3/2))) (((2 Sqrt[z] (15 + 4143 z + 3957 z^2 + 77 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^6 + (2 Sqrt[z] (15 + 4143 z + 3957 z^2 + 77 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^6 - ((-30 + 45 Sqrt[z] + 585 z + 3558 z^(3/2) + 1416 z^2 + 2541 z^(5/2) + 77 z^3) EllipticK[(1/2) (1 - Sqrt[z])])/((-1 + Sqrt[z])^6 (1 + Sqrt[z])^5) - ((-30 - 45 Sqrt[z] + 585 z - 3558 z^(3/2) + 1416 z^2 - 2541 z^(5/2) + 77 z^3) EllipticK[(1/2) (1 + Sqrt[z])])/ ((-1 + Sqrt[z])^5 (1 + Sqrt[z])^6)) Gamma[1/4]^2)










Standard Form





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MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["15", "4"], ",", FractionBox["19", "4"], ",", FractionBox["5", "2"], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["4143", " ", "z"]], "+", RowBox[List["3957", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["77", " ", 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"]], ")"]], "6"]], "+", FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["4143", " ", "z"]], "+", RowBox[List["3957", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["77", " ", 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"]], ")"]], "6"]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "+", RowBox[List["45", " ", SqrtBox["z"]]], "+", RowBox[List["585", " ", "z"]], "+", RowBox[List["3558", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["1416", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2541", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["77", " ", 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"]]], ")"]], "6"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "5"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "30"]], "-", RowBox[List["45", " ", SqrtBox["z"]]], "+", RowBox[List["585", " ", "z"]], "-", RowBox[List["3558", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["1416", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2541", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["77", " ", 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"]]], ")"]], "5"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "6"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]], "2"]]], RowBox[List["17787", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]]]]]]]










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





2007-05-02