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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[-(13/8), 6, -(5/8), -z] == (1/10485760) (13 (-((8 (1277155 + 4375892 z + 5925930 z^2 + 3647460 z^3 + 853035 z^4))/ (1 + z)^5) - 17913735 (-(8/13) + (8 z)/5 + (-1)^(1/8) z^(13/8) (I Log[1 - (-1)^(1/8) z^(1/8)] - I Log[1 + (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] - Log[1 - (-1)^(5/8) z^(1/8)] + Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 13 8 , 6 ; - 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["13", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["6", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox["5", "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 10485760 ( 13 ( - 8 ( 853035 z 4 + 3647460 z 3 + 5925930 z 2 + 4375892 z + 1277155 ) ( z + 1 ) 5 - 17913735 ( - 1 8 ( log ( 1 - - 1 8 z 8 ) - log ( - 1 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 5 / 8 z 8 ) + log ( ( - 1 ) 5 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 13 / 8 + 8 z 5 - 8 13 ) ) ) HypergeometricPFQ -1 13 8 6 -1 5 8 -1 z 1 10485760 13 -1 8 853035 z 4 3647460 z 3 5925930 z 2 4375892 z 1277155 z 1 5 -1 -1 17913735 -1 1 8 1 -1 -1 1 8 z 1 8 -1 -1 1 8 z 1 8 1 -1 -1 3 4 1 -1 -1 3 8 z 1 8 -1 3 4 -1 3 8 z 1 8 1 -1 1 -1 -1 5 8 z 1 8 -1 5 8 z 1 8 1 -1 1 4 1 -1 -1 7 8 z 1 8 -1 -1 1 4 -1 7 8 z 1 8 1 z 13 8 8 z 5 -1 -1 8 13 [/itex]

 Rule Form

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

 2007-05-02