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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.9480.01

 Input Form

 Hypergeometric2F1[-(23/4), 1/4, 17/4, z] == (1/(721554505728 z^(13/4))) (13 (-8 (1 - z)^(3/4) z^(1/4) (-7571025 + 84795480 z - 514156720 z^2 - 1916640768 z^3 + 1126175232 z^4 - 590921728 z^5 + 220495872 z^6 - 50331648 z^7 + 5242880 z^8) - 3028410 Sqrt[2] (-5 + 60 z - 384 z^2 + 3584 z^3) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 3028410 Sqrt[2] (-5 + 60 z - 384 z^2 + 3584 z^3) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))] - 1514205 Sqrt[2] (-5 + 60 z - 384 z^2 + 3584 z^3) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]] + 1514205 Sqrt[2] (-5 + 60 z - 384 z^2 + 3584 z^3) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))

 Standard Form

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 MathML Form

 2 F 1 ( - 23 4 , 1 4 ; 17 4 ; 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["23", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["17", "4"], 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 721554505728 z 13 / 4 ( 13 ( - 8 ( 1 - z ) 3 / 4 z 4 ( 5242880 z 8 - 50331648 z 7 + 220495872 z 6 - 590921728 z 5 + 1126175232 z 4 - 1916640768 z 3 - 514156720 z 2 + 84795480 z - 7571025 ) - 3028410 2 ( 3584 z 3 - 384 z 2 + 60 z - 5 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) - 3028410 2 ( 3584 z 3 - 384 z 2 + 60 z - 5 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) - 1514205 2 ( 3584 z 3 - 384 z 2 + 60 z - 5 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) + 1514205 2 ( 3584 z 3 - 384 z 2 + 60 z - 5 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) ) ) HypergeometricPFQ -1 23 4 1 4 17 4 z 1 721554505728 z 13 4 -1 13 -8 1 -1 z 3 4 z 1 4 5242880 z 8 -1 50331648 z 7 220495872 z 6 -1 590921728 z 5 1126175232 z 4 -1 1916640768 z 3 -1 514156720 z 2 84795480 z -7571025 -1 3028410 2 1 2 3584 z 3 -1 384 z 2 60 z -5 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 3028410 2 1 2 3584 z 3 -1 384 z 2 60 z -5 z 1 4 2 1 2 1 -1 z 1 4 -1 1 -1 z 1 4 2 1 2 1 -1 z 1 4 -1 -1 1514205 2 1 2 3584 z 3 -1 384 z 2 60 z -5 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 1514205 2 1 2 3584 z 3 -1 384 z 2 60 z -5 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 [/itex]

 Rule Form

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

 2007-05-02