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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.aj2w.01

 Input Form

 Hypergeometric2F1[3/4, 7/2, 6, z] == (1/(9945 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (2048 Sqrt[2] (-2 (512 - 752 z + 149 z^2 + 40 z^3 + 21 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (512 - 752 z + 149 z^2 + 40 z^3 + 21 z^4) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-512 + 496 z + 19 z^2 + 7 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (512 - 752 z + 149 z^2 + 40 z^3 + 21 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (512 - 752 z + 149 z^2 + 40 z^3 + 21 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (512 - 752 z + 149 z^2 + 40 z^3 + 21 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox["3", "4"], ",", FractionBox["7", "2"], ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["9945", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["2048", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List["512", "-", RowBox[List["752", " ", "z"]], "+", RowBox[List["149", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List["2", " ", SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["512", "-", RowBox[List["752", " ", "z"]], "+", RowBox[List["149", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "512"]], "+", RowBox[List["496", " ", "z"]], "+", RowBox[List["19", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["7", " ", SuperscriptBox["z", "3"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["512", "-", RowBox[List["752", " ", "z"]], "+", RowBox[List["149", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], " ", RowBox[List["(", RowBox[List["512", "-", RowBox[List["752", " ", "z"]], "+", RowBox[List["149", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]], "+", RowBox[List[SqrtBox[RowBox[List["1", "-", "z"]]], " ", RowBox[List["(", RowBox[List["512", "-", RowBox[List["752", " ", "z"]], "+", RowBox[List["149", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["40", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["21", " ", SuperscriptBox["z", "4"]]]]], ")"]], " ", RowBox[List["EllipticK", "[", RowBox[List[FractionBox["1", "2"], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List["1", "/", "4"]]], RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 2 F 1 ( 3 4 , 7 2 ; 6 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["7", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["6", 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 9945 π 1 - z + 1 z 5 ( 2048 2 ( - 2 1 - z ( 21 z 4 + 40 z 3 + 149 z 2 - 752 z + 512 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - 2 ( 21 z 4 + 40 z 3 + 149 z 2 - 752 z + 512 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 1 - z ) 3 / 4 ( 7 z 3 + 19 z 2 + 496 z - 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z ( 21 z 4 + 40 z 3 + 149 z 2 - 752 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + 1 - z 4 ( 21 z 4 + 40 z 3 + 149 z 2 - 752 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 21 z 4 + 40 z 3 + 149 z 2 - 752 z + 512 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ 3 4 7 2 6 z 1 9945 1 -1 z 1 2 1 1 2 z 5 -1 2048 2 1 2 -2 1 -1 z 1 2 21 z 4 40 z 3 149 z 2 -1 752 z 512 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 2 21 z 4 40 z 3 149 z 2 -1 752 z 512 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 3 4 7 z 3 19 z 2 496 z -512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 2 21 z 4 40 z 3 149 z 2 -1 752 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 1 4 21 z 4 40 z 3 149 z 2 -1 752 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 21 z 4 40 z 3 149 z 2 -1 752 z 512 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 [/itex]

 Rule Form

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

 2007-05-02