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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b4c9.01

 Input Form

 Hypergeometric2F1[5, 6, 23/5, z] == (39 (728 - 5145 z + 17850 z^2 + 191125 z^3 + 7500 z^4))/ (9765625 (-1 + z)^6 z^3) + (1638 Sqrt[10 - 2 Sqrt[5]] (-26 + 200 z - 750 z^2 + 2500 z^3 + 3125 z^4) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (48828125 (1 - z)^(32/5) z^(18/5)) - (1638 Sqrt[2 (5 + Sqrt[5])] (-26 + 200 z - 750 z^2 + 2500 z^3 + 3125 z^4) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (48828125 (1 - z)^(32/5) z^(18/5)) + (3276 (-26 + 200 z - 750 z^2 + 2500 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(48828125 (1 - z)^(32/5) z^(18/5)) - (819 (1 + Sqrt[5]) (-26 + 200 z - 750 z^2 + 2500 z^3 + 3125 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(48828125 (1 - z)^(32/5) z^(18/5)) + (819 (-1 + Sqrt[5]) (-26 + 200 z - 750 z^2 + 2500 z^3 + 3125 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(48828125 (1 - z)^(32/5) z^(18/5))

 Standard Form

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 MathML Form

 2 F 1 ( 5 , 6 ; 23 5 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["5", 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[FractionBox["23", "5"], 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] 39 ( 7500 z 4 + 191125 z 3 + 17850 z 2 - 5145 z + 728 ) 9765625 ( z - 1 ) 6 z 3 + ( 1638 10 - 2 5 ( 3125 z 4 + 2500 z 3 - 750 z 2 + 200 z - 26 ) tan - 1 ( 1 - ( 1 - 5 ) z 5 4 1 - z 5 , - 5 8 + 5 8 z 5 1 - z 5 ) ) / ( 48828125 ( 1 - z ) 32 / 5 z 18 / 5 ) - ( 1638 2 ( 5 + 5 ) ( 3125 z 4 + 2500 z 3 - 750 z 2 + 200 z - 26 ) tan - 1 ( 1 - ( 1 + 5 ) z 5 4 1 - z 5 , - 5 8 - 5 8 z 5 1 - z 5 ) ) / ( 48828125 ( 1 - z ) 32 / 5 z 18 / 5 ) + 3276 ( 3125 z 4 + 2500 z 3 - 750 z 2 + 200 z - 26 ) log ( z 5 1 - z 5 + 1 ) 48828125 ( 1 - z ) 32 / 5 z 18 / 5 - 819 ( 1 + 5 ) ( 3125 z 4 + 2500 z 3 - 750 z 2 + 200 z - 26 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 - 5 ) z 5 2 1 - z 5 + 1 ) 48828125 ( 1 - z ) 32 / 5 z 18 / 5 + 819 ( - 1 + 5 ) ( 3125 z 4 + 2500 z 3 - 750 z 2 + 200 z - 26 ) log ( z 2 / 5 ( 1 - z ) 2 / 5 - ( 1 + 5 ) z 5 2 1 - z 5 + 1 ) 48828125 ( 1 - z ) 32 / 5 z 18 / 5 HypergeometricPFQ 5 6 23 5 z 39 7500 z 4 191125 z 3 17850 z 2 -1 5145 z 728 9765625 z -1 6 z 3 -1 1638 10 -1 2 5 1 2 1 2 3125 z 4 2500 z 3 -1 750 z 2 200 z -26 1 -1 1 -1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 48828125 1 -1 z 32 5 z 18 5 -1 -1 1638 2 5 5 1 2 1 2 3125 z 4 2500 z 3 -1 750 z 2 200 z -26 1 -1 1 5 1 2 z 1 5 4 1 -1 z 1 5 -1 -1 5 8 -1 5 1 2 8 -1 1 2 z 1 5 1 -1 z 1 5 -1 48828125 1 -1 z 32 5 z 18 5 -1 3276 3125 z 4 2500 z 3 -1 750 z 2 200 z -26 z 1 5 1 -1 z 1 5 -1 1 48828125 1 -1 z 32 5 z 18 5 -1 -1 819 1 5 1 2 3125 z 4 2500 z 3 -1 750 z 2 200 z -26 z 2 5 1 -1 z 2 5 -1 -1 1 -1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 48828125 1 -1 z 32 5 z 18 5 -1 819 -1 5 1 2 3125 z 4 2500 z 3 -1 750 z 2 200 z -26 z 2 5 1 -1 z 2 5 -1 -1 1 5 1 2 z 1 5 2 1 -1 z 1 5 -1 1 48828125 1 -1 z 32 5 z 18 5 -1 [/itex]

 Rule Form

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

 2007-05-02