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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(1/4), 3/2, 6, z] == (1/(487305 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (1024 Sqrt[2] (2 (-1024 + 4576 z - 7802 z^2 + 5965 z^3 - 1400 z^4 + 840 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-1024 + 4576 z - 7802 z^2 + 5965 z^3 - 1400 z^4 + 840 z^5) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (1024 - 4064 z + 5930 z^2 - 3555 z^3 + 280 z^4) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (-1024 + 4576 z - 7802 z^2 + 5965 z^3 - 1400 z^4 + 840 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (-1024 + 4576 z - 7802 z^2 + 5965 z^3 - 1400 z^4 + 840 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (-1024 + 4576 z - 7802 z^2 + 5965 z^3 - 1400 z^4 + 840 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], ",", FractionBox["3", "2"], ",", "6", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["487305", " ", "\[Pi]", " ", SqrtBox[RowBox[List["1", "+", SqrtBox[RowBox[List["1", "-", "z"]]]]]], " ", SuperscriptBox["z", "5"]]]], RowBox[List["(", RowBox[List["1024", " ", SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1024"]], "+", RowBox[List["4576", " ", "z"]], "-", RowBox[List["7802", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5965", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["840", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[RowBox[List["-", "1024"]], "+", RowBox[List["4576", " ", "z"]], "-", RowBox[List["7802", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5965", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["840", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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["1024", "-", RowBox[List["4064", " ", "z"]], "+", RowBox[List["5930", " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["3555", " ", SuperscriptBox["z", "3"]]], "+", RowBox[List["280", " ", 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[RowBox[List["(", RowBox[List[RowBox[List["-", "1024"]], "+", RowBox[List["4576", " ", "z"]], "-", RowBox[List["7802", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5965", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["840", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[RowBox[List["-", "1024"]], "+", RowBox[List["4576", " ", "z"]], "-", RowBox[List["7802", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5965", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["840", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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[RowBox[List["-", "1024"]], "+", RowBox[List["4576", " ", "z"]], "-", RowBox[List["7802", " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["5965", " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["1400", " ", SuperscriptBox["z", "4"]]], "+", RowBox[List["840", " ", SuperscriptBox["z", "5"]]]]], ")"]], " ", 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 ( - 1 4 , 3 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[RowBox[List["-", FractionBox["1", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "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 487305 π 1 - z + 1 z 5 ( 1024 2 ( 2 1 - z ( 840 z 5 - 1400 z 4 + 5965 z 3 - 7802 z 2 + 4576 z - 1024 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + 2 ( 840 z 5 - 1400 z 4 + 5965 z 3 - 7802 z 2 + 4576 z - 1024 ) E ( 1 2 - 1 - z 4 1 - z + 1 ) + ( 1 - z ) 3 / 4 ( 280 z 4 - 3555 z 3 + 5930 z 2 - 4064 z + 1024 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z ( 840 z 5 - 1400 z 4 + 5965 z 3 - 7802 z 2 + 4576 z - 1024 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - 1 - z 4 ( 840 z 5 - 1400 z 4 + 5965 z 3 - 7802 z 2 + 4576 z - 1024 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) - ( 840 z 5 - 1400 z 4 + 5965 z 3 - 7802 z 2 + 4576 z - 1024 ) K ( 1 2 - 1 - z 4 1 - z + 1 ) ) ) HypergeometricPFQ -1 1 4 3 2 6 z 1 487305 1 -1 z 1 2 1 1 2 z 5 -1 1024 2 1 2 2 1 -1 z 1 2 840 z 5 -1 1400 z 4 5965 z 3 -1 7802 z 2 4576 z -1024 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 2 840 z 5 -1 1400 z 4 5965 z 3 -1 7802 z 2 4576 z -1024 EllipticE 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 1 -1 z 3 4 280 z 4 -1 3555 z 3 5930 z 2 -1 4064 z 1024 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 2 840 z 5 -1 1400 z 4 5965 z 3 -1 7802 z 2 4576 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 1 -1 z 1 4 840 z 5 -1 1400 z 4 5965 z 3 -1 7802 z 2 4576 z -1024 EllipticK 1 2 -1 1 -1 z 1 4 1 -1 z 1 2 1 -1 -1 840 z 5 -1 1400 z 4 5965 z 3 -1 7802 z 2 4576 z -1024 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