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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 1, 41/8, z] == (1/(262144 z^(33/8))) (11 (-1)^(1/4) (30600 (-1)^(3/4) z^(1/8) - 119000 (-1)^(3/4) z^(9/8) + 171800 (-1)^(3/4) z^(17/8) - 107976 (-1)^(3/4) z^(25/8) + 3825 (-1)^(3/4) (-1 + z)^4 Log[1 - z^(1/8)] + 3825 (-1)^(1/4) (-1 + z)^4 Log[1 - I z^(1/8)] - 3825 (-1)^(1/4) Log[1 + I z^(1/8)] + 15300 (-1)^(1/4) z Log[1 + I z^(1/8)] - 22950 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 15300 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] - 3825 (-1)^(1/4) z^4 Log[1 + I z^(1/8)] - 3825 (-1)^(3/4) Log[1 + z^(1/8)] + 15300 (-1)^(3/4) z Log[1 + z^(1/8)] - 22950 (-1)^(3/4) z^2 Log[1 + z^(1/8)] + 15300 (-1)^(3/4) z^3 Log[1 + z^(1/8)] - 3825 (-1)^(3/4) z^4 Log[1 + z^(1/8)] + 3825 I Log[1 - (-1)^(1/4) z^(1/8)] - 15300 I z Log[1 - (-1)^(1/4) z^(1/8)] + 22950 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] - 15300 I z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 3825 I z^4 Log[1 - (-1)^(1/4) z^(1/8)] - 3825 I Log[1 + (-1)^(1/4) z^(1/8)] + 15300 I z Log[1 + (-1)^(1/4) z^(1/8)] - 22950 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] + 15300 I z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 3825 I z^4 Log[1 + (-1)^(1/4) z^(1/8)] + 3825 Log[1 - (-1)^(3/4) z^(1/8)] - 15300 z Log[1 - (-1)^(3/4) z^(1/8)] + 22950 z^2 Log[1 - (-1)^(3/4) z^(1/8)] - 15300 z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 3825 z^4 Log[1 - (-1)^(3/4) z^(1/8)] - 3825 Log[1 + (-1)^(3/4) z^(1/8)] + 15300 z Log[1 + (-1)^(3/4) z^(1/8)] - 22950 z^2 Log[1 + (-1)^(3/4) z^(1/8)] + 15300 z^3 Log[1 + (-1)^(3/4) z^(1/8)] - 3825 z^4 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 1 ; 41 8 ; 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", "8"], 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["41", "8"], 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 262144 z 33 / 8 ( 11 - 1 4 ( 3825 ( - 1 ) 3 / 4 log ( 1 - z 8 ) ( z - 1 ) 4 + 3825 - 1 4 log ( 1 - z 8 ) ( z - 1 ) 4 - 107976 ( - 1 ) 3 / 4 z 25 / 8 + 171800 ( - 1 ) 3 / 4 z 17 / 8 - 119000 ( - 1 ) 3 / 4 z 9 / 8 - 3825 - 1 4 z 4 log ( z 8 + 1 ) + 15300 - 1 4 z 3 log ( z 8 + 1 ) - 22950 - 1 4 z 2 log ( z 8 + 1 ) + 15300 - 1 4 z log ( z 8 + 1 ) - 3825 - 1 4 log ( z 8 + 1 ) - 3825 ( - 1 ) 3 / 4 z 4 log ( z 8 + 1 ) + 15300 ( - 1 ) 3 / 4 z 3 log ( z 8 + 1 ) - 22950 ( - 1 ) 3 / 4 z 2 log ( z 8 + 1 ) + 15300 ( - 1 ) 3 / 4 z log ( z 8 + 1 ) - 3825 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 3825 z 4 log ( 1 - - 1 4 z 8 ) - 15300 z 3 log ( 1 - - 1 4 z 8 ) + 22950 z 2 log ( 1 - - 1 4 z 8 ) - 15300 z log ( 1 - - 1 4 z 8 ) + 3825 log ( 1 - - 1 4 z 8 ) - 3825 z 4 log ( - 1 4 z 8 + 1 ) + 15300 z 3 log ( - 1 4 z 8 + 1 ) - 22950 z 2 log ( - 1 4 z 8 + 1 ) + 15300 z log ( - 1 4 z 8 + 1 ) - 3825 log ( - 1 4 z 8 + 1 ) + 3825 z 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 15300 z 3 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 22950 z 2 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 15300 z log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 3825 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 3825 z 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 15300 z 3 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 22950 z 2 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 15300 z log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 3825 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 30600 ( - 1 ) 3 / 4 z 8 ) ) HypergeometricPFQ 1 8 1 41 8 z 1 262144 z 33 8 -1 11 -1 1 4 3825 -1 3 4 1 -1 z 1 8 z -1 4 3825 -1 1 4 1 -1 z 1 8 z -1 4 -1 107976 -1 3 4 z 25 8 171800 -1 3 4 z 17 8 -1 119000 -1 3 4 z 9 8 -1 3825 -1 1 4 z 4 z 1 8 1 15300 -1 1 4 z 3 z 1 8 1 -1 22950 -1 1 4 z 2 z 1 8 1 15300 -1 1 4 z z 1 8 1 -1 3825 -1 1 4 z 1 8 1 -1 3825 -1 3 4 z 4 z 1 8 1 15300 -1 3 4 z 3 z 1 8 1 -1 22950 -1 3 4 z 2 z 1 8 1 15300 -1 3 4 z z 1 8 1 -1 3825 -1 3 4 z 1 8 1 3825 z 4 1 -1 -1 1 4 z 1 8 -1 15300 z 3 1 -1 -1 1 4 z 1 8 22950 z 2 1 -1 -1 1 4 z 1 8 -1 15300 z 1 -1 -1 1 4 z 1 8 3825 1 -1 -1 1 4 z 1 8 -1 3825 z 4 -1 1 4 z 1 8 1 15300 z 3 -1 1 4 z 1 8 1 -1 22950 z 2 -1 1 4 z 1 8 1 15300 z -1 1 4 z 1 8 1 -1 3825 -1 1 4 z 1 8 1 3825 z 4 1 -1 -1 3 4 z 1 8 -1 15300 z 3 1 -1 -1 3 4 z 1 8 22950 z 2 1 -1 -1 3 4 z 1 8 -1 15300 z 1 -1 -1 3 4 z 1 8 3825 1 -1 -1 3 4 z 1 8 -1 3825 z 4 -1 3 4 z 1 8 1 15300 z 3 -1 3 4 z 1 8 1 -1 22950 z 2 -1 3 4 z 1 8 1 15300 z -1 3 4 z 1 8 1 -1 3825 -1 3 4 z 1 8 1 30600 -1 3 4 z 1 8 [/itex]

 Rule Form

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

 2007-05-02