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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.9016.01

 Input Form

 Hypergeometric2F1[-(23/4), -(19/4), -(15/4), z] == ((1 - z)^(3/4) (4620 - 30184 z + 86772 z^2 - 151632 z^3 + 236724 z^4 + 21945 z^5))/4620 - (437 z^(19/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(8 Sqrt[2]) - (437 z^(19/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(8 Sqrt[2]) - (437 z^(19/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(16 Sqrt[2]) + (437 z^(19/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(16 Sqrt[2])

 Standard Form

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 MathML Form

 2 F 1 ( - 23 4 , - 19 4 ; - 15 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[RowBox[List["-", FractionBox["19", "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["15", "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] - 437 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 19 / 4 8 2 - 437 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 19 / 4 8 2 - 437 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 19 / 4 16 2 + 437 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 19 / 4 16 2 + ( 1 - z ) 3 / 4 ( 21945 z 5 + 236724 z 4 - 151632 z 3 + 86772 z 2 - 30184 z + 4620 ) 4620 HypergeometricPFQ -1 23 4 -1 19 4 -1 15 4 z -1 437 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 z 19 4 8 2 1 2 -1 -1 437 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 z 19 4 8 2 1 2 -1 -1 437 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 19 4 16 2 1 2 -1 437 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 19 4 16 2 1 2 -1 1 -1 z 3 4 21945 z 5 236724 z 4 -1 151632 z 3 86772 z 2 -1 30184 z 4620 4620 -1 [/itex]

 Rule Form

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

 2007-05-02