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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(3/4), -(3/4), -(9/2), z] == (1/(3360 Pi^(3/2))) (((2 Sqrt[z] (-1680 + 4620 z - 4089 z^2 + 1117 z^3) EllipticE[(1/2) (1 - Sqrt[z])])/(-1 + z)^3 - (2 Sqrt[z] (-1680 + 4620 z - 4089 z^2 + 1117 z^3) EllipticE[(1/2) (1 + Sqrt[z])])/(-1 + z)^3 + (1/((-1 + Sqrt[z])^3 (1 + Sqrt[z])^2)) ((-3360 + 5040 Sqrt[z] + 6720 z - 11340 z^(3/2) - 3390 z^2 + 7479 z^(5/2) + 38 z^3 - 1155 z^(7/2)) EllipticK[(1/2) (1 - Sqrt[z])]) + (1/((-1 + Sqrt[z])^2 (1 + Sqrt[z])^3)) ((3360 + 5040 Sqrt[z] - 6720 z - 11340 z^(3/2) + 3390 z^2 + 7479 z^(5/2) - 38 z^3 - 1155 z^(7/2)) EllipticK[(1/2) (1 + Sqrt[z])])) Gamma[3/4]^2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["3", "4"]]], ",", RowBox[List["-", FractionBox["3", "4"]]], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["3360", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["4620", " ", "z"]], "-", RowBox[List["4089", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1117", " ", 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["-", "1680"]], "+", RowBox[List["4620", " ", "z"]], "-", RowBox[List["4089", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1117", " ", 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"]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "2"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "3360"]], "+", RowBox[List["5040", " ", SqrtBox["z"]]], "+", RowBox[List["6720", " ", "z"]], "-", RowBox[List["11340", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["3390", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7479", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["38", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1155", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SqrtBox["z"]]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]], "3"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["3360", "+", RowBox[List["5040", " ", SqrtBox["z"]]], "-", RowBox[List["6720", " ", "z"]], "-", RowBox[List["11340", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["3390", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7479", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["38", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1155", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SqrtBox["z"]]], ")"]]]], "]"]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]], "2"]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( - 3 4 , - 3 4 ; - 9 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["3", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["9", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] 1 3360 π 3 / 2 ( ( 2 z ( 1117 z 3 - 4089 z 2 + 4620 z - 1680 ) E ( 1 2 ( 1 - z ) ) ( z - 1 ) 3 - 2 z ( 1117 z 3 - 4089 z 2 + 4620 z - 1680 ) E ( 1 2 ( z + 1 ) ) ( z - 1 ) 3 + 1 ( z - 1 ) 3 ( z + 1 ) 2 ( - 1155 z 7 / 2 + 38 z 3 + 7479 z 5 / 2 - 3390 z 2 - 11340 z 3 / 2 + 6720 z + 5040 z - 3360 ) K ( 1 2 ( 1 - z ) ) + 1 ( z - 1 ) 2 ( z + 1 ) 3 ( - 1155 z 7 / 2 - 38 z 3 + 7479 z 5 / 2 + 3390 z 2 - 11340 z 3 / 2 - 6720 z + 5040 z + 3360 ) K ( 1 2 ( z + 1 ) ) ) Γ ( 3 4 ) 2 ) HypergeometricPFQ -1 3 4 -1 3 4 -1 9 2 z 1 3360 3 2 -1 2 z 1 2 1117 z 3 -1 4089 z 2 4620 z -1680 EllipticE 1 2 1 -1 z 1 2 z -1 3 -1 -1 2 z 1 2 1117 z 3 -1 4089 z 2 4620 z -1680 EllipticE 1 2 z 1 2 1 z -1 3 -1 1 z 1 2 -1 3 z 1 2 1 2 -1 -1155 z 7 2 38 z 3 7479 z 5 2 -1 3390 z 2 -1 11340 z 3 2 6720 z 5040 z 1 2 -3360 EllipticK 1 2 1 -1 z 1 2 1 z 1 2 -1 2 z 1 2 1 3 -1 -1155 z 7 2 -1 38 z 3 7479 z 5 2 3390 z 2 -1 11340 z 3 2 -1 6720 z 5040 z 1 2 3360 EllipticK 1 2 z 1 2 1 Gamma 3 4 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["3", "4"]]], ",", RowBox[List["-", FractionBox["3", "4"]]], ",", RowBox[List["-", FractionBox["9", "2"]]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1680"]], "+", RowBox[List["4620", " ", "z"]], "-", RowBox[List["4089", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1117", " ", 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["-", "1680"]], "+", RowBox[List["4620", " ", "z"]], "-", RowBox[List["4089", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["1117", " ", 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[RowBox[List["-", "3360"]], "+", RowBox[List["5040", " ", SqrtBox["z"]]], "+", RowBox[List["6720", " ", "z"]], "-", RowBox[List["11340", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "-", RowBox[List["3390", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7479", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["38", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1155", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", 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["3360", "+", RowBox[List["5040", " ", SqrtBox["z"]]], "-", RowBox[List["6720", " ", "z"]], "-", RowBox[List["11340", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "+", RowBox[List["3390", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7479", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["38", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1155", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]], ")"]], " ", 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["3", "4"], "]"]], "2"]]], RowBox[List["3360", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]]]]]]

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

 2007-05-02