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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[1/8, 2, 25/8, z] == (1/(8192 z^(17/8))) (153 (-1)^(1/4) (-72 (-1)^(3/4) z^(1/8) + 8 (-1)^(3/4) z^(9/8) + (-1)^(3/4) (-9 + 2 z + 7 z^2) Log[1 - z^(1/8)] + (-1)^(1/4) (-9 + 2 z + 7 z^2) Log[1 - I z^(1/8)] + 9 (-1)^(1/4) Log[1 + I z^(1/8)] - 2 (-1)^(1/4) z Log[1 + I z^(1/8)] - 7 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 9 (-1)^(3/4) Log[1 + z^(1/8)] - 2 (-1)^(3/4) z Log[1 + z^(1/8)] - 7 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 9 I Log[1 - (-1)^(1/4) z^(1/8)] + 2 I z Log[1 - (-1)^(1/4) z^(1/8)] + 7 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] + 9 I Log[1 + (-1)^(1/4) z^(1/8)] - 2 I z Log[1 + (-1)^(1/4) z^(1/8)] - 7 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] - 9 Log[1 - (-1)^(3/4) z^(1/8)] + 2 z Log[1 - (-1)^(3/4) z^(1/8)] + 7 z^2 Log[1 - (-1)^(3/4) z^(1/8)] + 9 Log[1 + (-1)^(3/4) z^(1/8)] - 2 z Log[1 + (-1)^(3/4) z^(1/8)] - 7 z^2 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 2 ; 25 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["25", "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 8192 z 17 / 8 ( 153 - 1 4 ( - 7 - 1 4 log ( z 8 + 1 ) z 2 - 7 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z 2 + 7 log ( 1 - - 1 4 z 8 ) z 2 - 7 log ( - 1 4 z 8 + 1 ) z 2 + 7 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z 2 - 7 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z 2 + 8 ( - 1 ) 3 / 4 z 9 / 8 - 2 - 1 4 log ( z 8 + 1 ) z - 2 ( - 1 ) 3 / 4 log ( z 8 + 1 ) z + 2 log ( 1 - - 1 4 z 8 ) z - 2 log ( - 1 4 z 8 + 1 ) z + 2 log ( 1 - ( - 1 ) 3 / 4 z 8 ) z - 2 log ( ( - 1 ) 3 / 4 z 8 + 1 ) z - 72 ( - 1 ) 3 / 4 z 8 + ( - 1 ) 3 / 4 ( 7 z 2 + 2 z - 9 ) log ( 1 - z 8 ) + - 1 4 ( 7 z 2 + 2 z - 9 ) log ( 1 - z 8 ) + 9 - 1 4 log ( z 8 + 1 ) + 9 ( - 1 ) 3 / 4 log ( z 8 + 1 ) - 9 log ( 1 - - 1 4 z 8 ) + 9 log ( - 1 4 z 8 + 1 ) - 9 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 9 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) HypergeometricPFQ 1 8 2 25 8 z 1 8192 z 17 8 -1 153 -1 1 4 -7 -1 1 4 z 1 8 1 z 2 -1 7 -1 3 4 z 1 8 1 z 2 7 1 -1 -1 1 4 z 1 8 z 2 -1 7 -1 1 4 z 1 8 1 z 2 7 1 -1 -1 3 4 z 1 8 z 2 -1 7 -1 3 4 z 1 8 1 z 2 8 -1 3 4 z 9 8 -1 2 -1 1 4 z 1 8 1 z -1 2 -1 3 4 z 1 8 1 z 2 1 -1 -1 1 4 z 1 8 z -1 2 -1 1 4 z 1 8 1 z 2 1 -1 -1 3 4 z 1 8 z -1 2 -1 3 4 z 1 8 1 z -1 72 -1 3 4 z 1 8 -1 3 4 7 z 2 2 z -9 1 -1 z 1 8 -1 1 4 7 z 2 2 z -9 1 -1 z 1 8 9 -1 1 4 z 1 8 1 9 -1 3 4 z 1 8 1 -1 9 1 -1 -1 1 4 z 1 8 9 -1 1 4 z 1 8 1 -1 9 1 -1 -1 3 4 z 1 8 9 -1 3 4 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02