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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 1, 33/8, z] == (1/(24576 z^(25/8))) (25 (-1)^(1/4) (-1224 (-1)^(3/4) z^(1/8) + 3536 (-1)^(3/4) z^(9/8) - 3336 (-1)^(3/4) z^(17/8) + 153 (-1)^(3/4) (-1 + z)^3 Log[1 - z^(1/8)] + 153 (-1)^(1/4) (-1 + z)^3 Log[1 - I z^(1/8)] + 153 (-1)^(1/4) Log[1 + I z^(1/8)] - 459 (-1)^(1/4) z Log[1 + I z^(1/8)] + 459 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] - 153 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] + 153 (-1)^(3/4) Log[1 + z^(1/8)] - 459 (-1)^(3/4) z Log[1 + z^(1/8)] + 459 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 153 (-1)^(3/4) z^3 Log[1 + z^(1/8)] - 153 I Log[1 - (-1)^(1/4) z^(1/8)] + 459 I z Log[1 - (-1)^(1/4) z^(1/8)] - 459 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] + 153 I z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 153 I Log[1 + (-1)^(1/4) z^(1/8)] - 459 I z Log[1 + (-1)^(1/4) z^(1/8)] + 459 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] - 153 I z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 153 Log[1 - (-1)^(3/4) z^(1/8)] + 459 z Log[1 - (-1)^(3/4) z^(1/8)] - 459 z^2 Log[1 - (-1)^(3/4) z^(1/8)] + 153 z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 153 Log[1 + (-1)^(3/4) z^(1/8)] - 459 z Log[1 + (-1)^(3/4) z^(1/8)] + 459 z^2 Log[1 + (-1)^(3/4) z^(1/8)] - 153 z^3 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 1 ; 33 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["33", "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 24576 z 25 / 8 ( 25 - 1 4 ( 153 ( - 1 ) 3 / 4 log ( 1 - z 8 ) ( z - 1 ) 3 + 153 - 1 4 log ( 1 - z 8 ) ( z - 1 ) 3 - 3336 ( - 1 ) 3 / 4 z 17 / 8 + 3536 ( - 1 ) 3 / 4 z 9 / 8 - 153 - 1 4 z 3 log ( z 8 + 1 ) + 459 - 1 4 z 2 log ( z 8 + 1 ) - 459 - 1 4 z log ( z 8 + 1 ) + 153 - 1 4 log ( z 8 + 1 ) - 153 ( - 1 ) 3 / 4 z 3 log ( z 8 + 1 ) + 459 ( - 1 ) 3 / 4 z 2 log ( z 8 + 1 ) - 459 ( - 1 ) 3 / 4 z log ( z 8 + 1 ) + 153 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 153 z 3 log ( 1 - - 1 4 z 8 ) - 459 z 2 log ( 1 - - 1 4 z 8 ) + 459 z log ( 1 - - 1 4 z 8 ) - 153 log ( 1 - - 1 4 z 8 ) - 153 z 3 log ( - 1 4 z 8 + 1 ) + 459 z 2 log ( - 1 4 z 8 + 1 ) - 459 z log ( - 1 4 z 8 + 1 ) + 153 log ( - 1 4 z 8 + 1 ) + 153 z 3 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 459 z 2 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 459 z log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 153 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 153 z 3 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 459 z 2 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 459 z log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 153 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 1224 ( - 1 ) 3 / 4 z 8 ) ) HypergeometricPFQ 1 8 1 33 8 z 1 24576 z 25 8 -1 25 -1 1 4 153 -1 3 4 1 -1 z 1 8 z -1 3 153 -1 1 4 1 -1 z 1 8 z -1 3 -1 3336 -1 3 4 z 17 8 3536 -1 3 4 z 9 8 -1 153 -1 1 4 z 3 z 1 8 1 459 -1 1 4 z 2 z 1 8 1 -1 459 -1 1 4 z z 1 8 1 153 -1 1 4 z 1 8 1 -1 153 -1 3 4 z 3 z 1 8 1 459 -1 3 4 z 2 z 1 8 1 -1 459 -1 3 4 z z 1 8 1 153 -1 3 4 z 1 8 1 153 z 3 1 -1 -1 1 4 z 1 8 -1 459 z 2 1 -1 -1 1 4 z 1 8 459 z 1 -1 -1 1 4 z 1 8 -1 153 1 -1 -1 1 4 z 1 8 -1 153 z 3 -1 1 4 z 1 8 1 459 z 2 -1 1 4 z 1 8 1 -1 459 z -1 1 4 z 1 8 1 153 -1 1 4 z 1 8 1 153 z 3 1 -1 -1 3 4 z 1 8 -1 459 z 2 1 -1 -1 3 4 z 1 8 459 z 1 -1 -1 3 4 z 1 8 -1 153 1 -1 -1 3 4 z 1 8 -1 153 z 3 -1 3 4 z 1 8 1 459 z 2 -1 3 4 z 1 8 1 -1 459 z -1 3 4 z 1 8 1 153 -1 3 4 z 1 8 1 -1 1224 -1 3 4 z 1 8 [/itex]

 Rule Form

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

 2007-05-02