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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[2, 4, -(15/4), z] == (1/4730880) (-((1/(-1 + z)^9) (8 (591360 - 6583808 z + 36083712 z^2 - 141785088 z^3 + 629404672 z^4 + 1067325297 z^5 + 60568200 z^6 - 2691920 z^7))) - (281642130 Sqrt[2] z^(19/4) (23 + 12 z) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(39/4) - (281642130 Sqrt[2] z^(19/4) (23 + 12 z) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(39/4) - (140821065 Sqrt[2] z^(19/4) (23 + 12 z) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(39/4) + (140821065 Sqrt[2] z^(19/4) (23 + 12 z) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/ (1 - z)^(39/4))

 Standard Form

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 MathML Form

 2 F 1 ( 2 , 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["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] 1 4730880 ( - 281642130 2 ( 12 z + 23 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 19 / 4 ( 1 - z ) 39 / 4 - 281642130 2 ( 12 z + 23 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 19 / 4 ( 1 - z ) 39 / 4 - 140821065 2 ( 12 z + 23 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 19 / 4 ( 1 - z ) 39 / 4 + 140821065 2 ( 12 z + 23 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 19 / 4 ( 1 - z ) 39 / 4 - 1 ( z - 1 ) 9 ( 8 ( - 2691920 z 7 + 60568200 z 6 + 1067325297 z 5 + 629404672 z 4 - 141785088 z 3 + 36083712 z 2 - 6583808 z + 591360 ) ) ) HypergeometricPFQ 2 4 -1 15 4 z 1 4730880 -1 281642130 2 1 2 12 z 23 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 1 -1 z 39 4 -1 -1 281642130 2 1 2 12 z 23 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 1 -1 z 39 4 -1 -1 140821065 2 1 2 12 z 23 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 1 -1 z 39 4 -1 140821065 2 1 2 12 z 23 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 1 -1 z 39 4 -1 -1 1 z -1 9 -1 8 -2691920 z 7 60568200 z 6 1067325297 z 5 629404672 z 4 -1 141785088 z 3 36083712 z 2 -1 6583808 z 591360 [/itex]

 Rule Form

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

 2007-05-02