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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.br57.01

 Input Form

 Hypergeometric2F1[-(11/8), 1, 13/8, -z] == -((1/(1024 z^(5/8))) (5 (-1)^(1/8) (152 (-1)^(7/8) z^(5/8) + 88 (-1)^(7/8) z^(13/8) - 33 (-1)^(1/4) (1 + z)^2 Log[1 - (-1)^(1/8) z^(1/8)] + 33 (-1)^(1/4) (1 + z)^2 Log[1 + (-1)^(1/8) z^(1/8)] + 33 Log[1 - (-1)^(3/8) z^(1/8)] + 66 z Log[1 - (-1)^(3/8) z^(1/8)] + 33 z^2 Log[1 - (-1)^(3/8) z^(1/8)] - 33 Log[1 + (-1)^(3/8) z^(1/8)] - 66 z Log[1 + (-1)^(3/8) z^(1/8)] - 33 z^2 Log[1 + (-1)^(3/8) z^(1/8)] + 33 (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + 66 (-1)^(3/4) z Log[1 - (-1)^(5/8) z^(1/8)] + 33 (-1)^(3/4) z^2 Log[1 - (-1)^(5/8) z^(1/8)] - 33 (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] - 66 (-1)^(3/4) z Log[1 + (-1)^(5/8) z^(1/8)] - 33 (-1)^(3/4) z^2 Log[1 + (-1)^(5/8) z^(1/8)] - 33 I Log[1 - (-1)^(7/8) z^(1/8)] - 66 I z Log[1 - (-1)^(7/8) z^(1/8)] - 33 I z^2 Log[1 - (-1)^(7/8) z^(1/8)] + 33 I Log[1 + (-1)^(7/8) z^(1/8)] + 66 I z Log[1 + (-1)^(7/8) z^(1/8)] + 33 I z^2 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( - 11 8 , 1 ; 13 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["13", "8"], 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 1024 z 5 / 8 ( 5 - 1 8 ( 33 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 33 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 33 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 33 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 33 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 33 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 88 ( - 1 ) 7 / 8 z 13 / 8 + 66 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z - 66 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z + 66 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z - 66 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z - 66 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z + 66 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 152 ( - 1 ) 7 / 8 z 5 / 8 - 33 - 1 4 ( z + 1 ) 2 log ( 1 - - 1 8 z 8 ) + 33 - 1 4 ( z + 1 ) 2 log ( - 1 8 z 8 + 1 ) + 33 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 33 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 33 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 33 ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 33 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 33 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ -1 11 8 1 13 8 -1 z -1 1 1024 z 5 8 -1 5 -1 1 8 33 1 -1 -1 3 8 z 1 8 z 2 -1 33 -1 3 8 z 1 8 1 z 2 33 -1 3 4 1 -1 -1 5 8 z 1 8 z 2 -1 33 -1 3 4 -1 5 8 z 1 8 1 z 2 -1 33 1 -1 -1 7 8 z 1 8 z 2 33 -1 7 8 z 1 8 1 z 2 88 -1 7 8 z 13 8 66 1 -1 -1 3 8 z 1 8 z -1 66 -1 3 8 z 1 8 1 z 66 -1 3 4 1 -1 -1 5 8 z 1 8 z -1 66 -1 3 4 -1 5 8 z 1 8 1 z -1 66 1 -1 -1 7 8 z 1 8 z 66 -1 7 8 z 1 8 1 z 152 -1 7 8 z 5 8 -1 33 -1 1 4 z 1 2 1 -1 -1 1 8 z 1 8 33 -1 1 4 z 1 2 -1 1 8 z 1 8 1 33 1 -1 -1 3 8 z 1 8 -1 33 -1 3 8 z 1 8 1 33 -1 3 4 1 -1 -1 5 8 z 1 8 -1 33 -1 3 4 -1 5 8 z 1 8 1 -1 33 1 -1 -1 7 8 z 1 8 33 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02