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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/5, 1, 26/5, -z] == (1/(12500 z^(21/5))) (7 (-2640 z^(1/5) - 10120 z^(6/5) - 14320 z^(11/5) - 8715 z^(16/5) + 528 (1 + z)^4 Log[1 + z^(1/5)] + 528 (-1)^(4/5) (1 + z)^4 Log[1 - (-1)^(1/5) z^(1/5)] - 528 (-1)^(3/5) Log[1 + (-1)^(2/5) z^(1/5)] - 2112 (-1)^(3/5) z Log[1 + (-1)^(2/5) z^(1/5)] - 3168 (-1)^(3/5) z^2 Log[1 + (-1)^(2/5) z^(1/5)] - 2112 (-1)^(3/5) z^3 Log[1 + (-1)^(2/5) z^(1/5)] - 528 (-1)^(3/5) z^4 Log[1 + (-1)^(2/5) z^(1/5)] + 528 (-1)^(2/5) Log[1 - (-1)^(3/5) z^(1/5)] + 2112 (-1)^(2/5) z Log[1 - (-1)^(3/5) z^(1/5)] + 3168 (-1)^(2/5) z^2 Log[1 - (-1)^(3/5) z^(1/5)] + 2112 (-1)^(2/5) z^3 Log[1 - (-1)^(3/5) z^(1/5)] + 528 (-1)^(2/5) z^4 Log[1 - (-1)^(3/5) z^(1/5)] - 528 (-1)^(1/5) Log[1 + (-1)^(4/5) z^(1/5)] - 2112 (-1)^(1/5) z Log[1 + (-1)^(4/5) z^(1/5)] - 3168 (-1)^(1/5) z^2 Log[1 + (-1)^(4/5) z^(1/5)] - 2112 (-1)^(1/5) z^3 Log[1 + (-1)^(4/5) z^(1/5)] - 528 (-1)^(1/5) z^4 Log[1 + (-1)^(4/5) z^(1/5)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 5 , 1 ; 26 5 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["1", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["26", "5"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "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 12500 z 21 / 5 ( 7 ( - 528 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 4 + 528 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 4 - 528 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 4 - 8715 z 16 / 5 - 2112 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 3 + 2112 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 3 - 2112 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 3 - 14320 z 11 / 5 - 3168 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z 2 + 3168 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z 2 - 3168 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z 2 - 10120 z 6 / 5 - 2112 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) z + 2112 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) z - 2112 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) z - 2640 z 5 + 528 ( z + 1 ) 4 log ( z 5 + 1 ) + 528 ( - 1 ) 4 / 5 ( z + 1 ) 4 log ( 1 - - 1 5 z 5 ) - 528 ( - 1 ) 3 / 5 log ( ( - 1 ) 2 / 5 z 5 + 1 ) + 528 ( - 1 ) 2 / 5 log ( 1 - ( - 1 ) 3 / 5 z 5 ) - 528 - 1 5 log ( ( - 1 ) 4 / 5 z 5 + 1 ) ) ) HypergeometricPFQ 1 5 1 26 5 -1 z 1 12500 z 21 5 -1 7 -528 -1 3 5 -1 2 5 z 1 5 1 z 4 528 -1 2 5 1 -1 -1 3 5 z 1 5 z 4 -1 528 -1 1 5 -1 4 5 z 1 5 1 z 4 -1 8715 z 16 5 -1 2112 -1 3 5 -1 2 5 z 1 5 1 z 3 2112 -1 2 5 1 -1 -1 3 5 z 1 5 z 3 -1 2112 -1 1 5 -1 4 5 z 1 5 1 z 3 -1 14320 z 11 5 -1 3168 -1 3 5 -1 2 5 z 1 5 1 z 2 3168 -1 2 5 1 -1 -1 3 5 z 1 5 z 2 -1 3168 -1 1 5 -1 4 5 z 1 5 1 z 2 -1 10120 z 6 5 -1 2112 -1 3 5 -1 2 5 z 1 5 1 z 2112 -1 2 5 1 -1 -1 3 5 z 1 5 z -1 2112 -1 1 5 -1 4 5 z 1 5 1 z -1 2640 z 1 5 528 z 1 4 z 1 5 1 528 -1 4 5 z 1 4 1 -1 -1 1 5 z 1 5 -1 528 -1 3 5 -1 2 5 z 1 5 1 528 -1 2 5 1 -1 -1 3 5 z 1 5 -1 528 -1 1 5 -1 4 5 z 1 5 1 [/itex]

 Rule Form

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

 2007-05-02