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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br53.01

 Input Form

 Hypergeometric2F1[-(11/8), 1, 5/8, z] == (33/64) (8/3 - (8/33) (3 + 11 z) + z^(3/8) (Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] - Log[1 + z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]) + z^(11/8) (-Log[1 - z^(1/8)] + I Log[1 - I z^(1/8)] - I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , 1 ; 5 8 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", FractionBox["11", "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["5", "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] 33 64 ( ( - log ( 1 - z 8 ) + log ( 1 - z 8 ) - log ( z 8 + 1 ) + log ( z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 11 / 8 + ( log ( 1 - z 8 ) - log ( 1 - z 8 ) + log ( z 8 + 1 ) - log ( z 8 + 1 ) + ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) z 3 / 8 - 8 33 ( 11 z + 3 ) + 8 3 ) HypergeometricPFQ -1 11 8 1 5 8 z 33 64 -1 1 -1 z 1 8 1 -1 z 1 8 -1 z 1 8 1 z 1 8 1 -1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 3 4 -1 1 4 z 1 8 1 -1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 1 4 -1 3 4 z 1 8 1 z 11 8 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -1 z 1 8 1 -1 3 4 1 -1 -1 1 4 z 1 8 -1 -1 3 4 -1 1 4 z 1 8 1 -1 1 4 1 -1 -1 3 4 z 1 8 -1 -1 1 4 -1 3 4 z 1 8 1 z 3 8 -1 8 33 11 z 3 8 3 [/itex]

 Rule Form

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

 2007-05-02