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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1, 2, -(13/4), z] == (1/6240) ((8 (780 - 5160 z + 15220 z^2 - 28688 z^3 + 84148 z^4 + 3315 z^5))/ (-1 + z)^6 - (139230 Sqrt[2] z^(17/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) - (139230 Sqrt[2] z^(17/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(25/4) + (69615 Sqrt[2] z^(17/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(25/4) - (69615 Sqrt[2] z^(17/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(25/4))

 Standard Form

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 MathML Form

 2 F 1 ( 1 , 2 ; - 13 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["2", 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["13", "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 6240 ( - 139230 2 tan - 1 ( 1 - z 4 2 1 - z 4 , - z 4 2 1 - z 4 ) z 17 / 4 ( 1 - z ) 25 / 4 - 139230 2 tan - 1 ( z 4 2 1 - z 4 + 1 , - z 4 2 1 - z 4 ) z 17 / 4 ( 1 - z ) 25 / 4 + 69615 2 log ( z 1 - z - 2 z 4 1 - z 4 + 1 ) z 17 / 4 ( 1 - z ) 25 / 4 - 69615 2 log ( z 1 - z + 2 z 4 1 - z 4 + 1 ) z 17 / 4 ( 1 - z ) 25 / 4 + 8 ( 3315 z 5 + 84148 z 4 - 28688 z 3 + 15220 z 2 - 5160 z + 780 ) ( z - 1 ) 6 ) HypergeometricPFQ 1 2 -1 13 4 z 1 6240 -1 139230 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 17 4 1 -1 z 25 4 -1 -1 139230 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 17 4 1 -1 z 25 4 -1 69615 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 17 4 1 -1 z 25 4 -1 -1 69615 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 17 4 1 -1 z 25 4 -1 8 3315 z 5 84148 z 4 -1 28688 z 3 15220 z 2 -1 5160 z 780 z -1 6 -1 [/itex]

 Rule Form

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

 2007-05-02