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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[2, 5, -(11/4), z] == (1/5046272) ((1/(-1 + z)^9) (8 (-630784 + 7970816 z - 55148544 z^2 + 388530176 z^3 + 1178391701 z^4 + 136673460 z^5 - 13810720 z^6 + 936320 z^7)) + (281642130 Sqrt[2] z^(15/4) (19 + 16 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^(15/4) (19 + 16 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^(15/4) (19 + 16 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^(15/4) (19 + 16 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 , 5 ; - 11 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["5", 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["11", "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 5046272 ( 281642130 2 ( 16 z + 19 ) tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 15 / 4 ( 1 - z ) 39 / 4 + 281642130 2 ( 16 z + 19 ) tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 15 / 4 ( 1 - z ) 39 / 4 + 140821065 2 ( 16 z + 19 ) log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 15 / 4 ( 1 - z ) 39 / 4 - 140821065 2 ( 16 z + 19 ) log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 15 / 4 ( 1 - z ) 39 / 4 + 1 ( z - 1 ) 9 ( 8 ( 936320 z 7 - 13810720 z 6 + 136673460 z 5 + 1178391701 z 4 + 388530176 z 3 - 55148544 z 2 + 7970816 z - 630784 ) ) ) HypergeometricPFQ 2 5 -1 11 4 z 1 5046272 281642130 2 1 2 16 z 19 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 15 4 1 -1 z 39 4 -1 281642130 2 1 2 16 z 19 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 15 4 1 -1 z 39 4 -1 140821065 2 1 2 16 z 19 z 1 2 1 -1 z 1 2 -1 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 15 4 1 -1 z 39 4 -1 -1 140821065 2 1 2 16 z 19 z 1 2 1 -1 z 1 2 -1 2 1 2 z 1 4 1 -1 z 1 4 -1 1 z 15 4 1 -1 z 39 4 -1 1 z -1 9 -1 8 936320 z 7 -1 13810720 z 6 136673460 z 5 1178391701 z 4 388530176 z 3 -1 55148544 z 2 7970816 z -630784 [/itex]

 Rule Form

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

 2007-05-02