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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[2, 3, -(7/4), z] == (1/7168) ((8 (896 - 8448 z + 56448 z^2 + 114729 z^3 + 4620 z^4))/ (-1 + z)^6 - (43890 Sqrt[2] z^(11/4) (15 + 8 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(27/4) - (43890 Sqrt[2] z^(11/4) (15 + 8 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(27/4) - (21945 Sqrt[2] z^(11/4) (15 + 8 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(27/4) + (21945 Sqrt[2] z^(11/4) (15 + 8 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(27/4))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 3 ; - 7 4 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["3", 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["7", "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 7168 ( - 43890 2 ( 8 z + 15 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 11 / 4 ( 1 - z ) 27 / 4 - 43890 2 ( 8 z + 15 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 11 / 4 ( 1 - z ) 27 / 4 - 21945 2 ( 8 z + 15 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 11 / 4 ( 1 - z ) 27 / 4 + 21945 2 ( 8 z + 15 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 11 / 4 ( 1 - z ) 27 / 4 + 8 ( 4620 z 4 + 114729 z 3 + 56448 z 2 - 8448 z + 896 ) ( z - 1 ) 6 ) HypergeometricPFQ 2 3 -1 7 4 z 1 7168 -1 43890 2 1 2 8 z 15 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 11 4 1 -1 z 27 4 -1 -1 43890 2 1 2 8 z 15 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 11 4 1 -1 z 27 4 -1 -1 21945 2 1 2 8 z 15 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 11 4 1 -1 z 27 4 -1 21945 2 1 2 8 z 15 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 11 4 1 -1 z 27 4 -1 8 4620 z 4 114729 z 3 56448 z 2 -1 8448 z 896 z -1 6 -1 [/itex]

 Rule Form

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

 2007-05-02