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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1, 6, -(7/4), z] == (1/2293760) ((1/(-1 + z)^8) (8 (286720 - 3276800 z + 25067520 z^2 + 35798455 z^3 - 15516116 z^4 + 5832288 z^5 - 1409408 z^6 + 157696 z^7)) - (281642130 Sqrt[2] z^(11/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(35/4) - (281642130 Sqrt[2] z^(11/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(35/4) - (140821065 Sqrt[2] z^(11/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(35/4) + (140821065 Sqrt[2] z^(11/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(35/4))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 6 ; - 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["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", 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 2293760 ( - 281642130 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 11 / 4 ( 1 - z ) 35 / 4 - 281642130 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 11 / 4 ( 1 - z ) 35 / 4 - 140821065 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 11 / 4 ( 1 - z ) 35 / 4 + 140821065 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 11 / 4 ( 1 - z ) 35 / 4 + 1 ( z - 1 ) 8 8 ( 157696 z 7 - 1409408 z 6 + 5832288 z 5 - 15516116 z 4 + 35798455 z 3 + 25067520 z 2 - 3276800 z + 286720 ) ) HypergeometricPFQ 1 6 -1 7 4 z 1 2293760 -1 281642130 2 1 2 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 35 4 -1 -1 281642130 2 1 2 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 35 4 -1 -1 140821065 2 1 2 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 35 4 -1 140821065 2 1 2 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 35 4 -1 1 z -1 8 -1 8 157696 z 7 -1 1409408 z 6 5832288 z 5 -1 15516116 z 4 35798455 z 3 25067520 z 2 -1 3276800 z 286720 [/itex]

 Rule Form

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

 2007-05-02