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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.b5ok.01

 Input Form

 Hypergeometric2F1[-(47/8), 5, 1/8, -z] == (1/68719476736) (45742515 (435643 (-(8/15) + (8 z)/7 + (-1)^(1/8) z^(15/8) ((-1)^(3/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] + I Log[1 - (-1)^(3/8) z^(1/8)] - I Log[1 + (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + Log[1 - (-1)^(7/8) z^(1/8)] - Log[1 + (-1)^(7/8) z^(1/8)])) + 4234230 (-(8/31) + (8 z)/23 - (8 z^2)/15 + (8 z^3)/7 + (-1)^(1/8) z^(31/8) ((-1)^(3/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] + I Log[1 - (-1)^(3/8) z^(1/8)] - I Log[1 + (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + Log[1 - (-1)^(7/8) z^(1/8)] - Log[1 + (-1)^(7/8) z^(1/8)])) + 1295679 (-(8/47) + (8 z)/39 - (8 z^2)/31 + (8 z^3)/23 - (8 z^4)/15 + (8 z^5)/7 + (-1)^(1/8) z^(47/8) ((-1)^(3/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] + I Log[1 - (-1)^(3/8) z^(1/8)] - I Log[1 + (-1)^(3/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] + Log[1 - (-1)^(7/8) z^(1/8)] - Log[1 + (-1)^(7/8) z^(1/8)])) + (27807/7) (8 + 7 (-1)^(7/8) z^(7/8) Log[1 - (-1)^(1/8) z^(1/8)] - 7 (-1)^(7/8) z^(7/8) Log[1 + (-1)^(1/8) z^(1/8)] + 7 (-1)^(5/8) z^(7/8) Log[1 - (-1)^(3/8) z^(1/8)] - 7 (-1)^(5/8) z^(7/8) Log[1 + (-1)^(3/8) z^(1/8)] + 7 (-1)^(3/8) z^(7/8) Log[1 - (-1)^(5/8) z^(1/8)] - 7 (-1)^(3/8) z^(7/8) Log[1 + (-1)^(5/8) z^(1/8)] + 7 (-1)^(1/8) z^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] - 7 (-1)^(1/8) z^(7/8) Log[1 + (-1)^(7/8) z^(1/8)]) - 2083510 (-(8/23) + (8 z)/15 - (8 z^2)/7 + (-1)^(1/8) z^(23/8) ((-(-1)^(3/4)) Log[1 - (-1)^(1/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] - I Log[1 - (-1)^(3/8) z^(1/8)] + I Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - Log[1 - (-1)^(7/8) z^(1/8)] + Log[1 + (-1)^(7/8) z^(1/8)])) - 3854235 (-(8/39) + (8 z)/31 - (8 z^2)/23 + (8 z^3)/15 - (8 z^4)/7 + (-1)^(1/8) z^(39/8) ((-(-1)^(3/4)) Log[1 - (-1)^(1/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(1/8) z^(1/8)] - I Log[1 - (-1)^(3/8) z^(1/8)] + I Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - Log[1 - (-1)^(7/8) z^(1/8)] + Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( - 47 8 , 5 ; 1 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["47", "8"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["5", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["1", "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 68719476736 ( 45742515 ( 435643 ( - 1 8 ( ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 3 / 8 z 8 ) - log ( ( - 1 ) 3 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 15 / 8 + 8 z 7 - 8 15 ) + 4234230 ( - 1 8 ( ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 3 / 8 z 8 ) - log ( ( - 1 ) 3 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 31 / 8 + 8 z 3 7 - 8 z 2 15 + 8 z 23 - 8 31 ) + 1295679 ( - 1 8 ( ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) - ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 3 / 8 z 8 ) - log ( ( - 1 ) 3 / 8 z 8 + 1 ) + - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 47 / 8 + 8 z 5 7 - 8 z 4 15 + 8 z 3 23 - 8 z 2 31 + 8 z 39 - 8 47 ) + 27807 7 ( 7 ( - 1 ) 7 / 8 z 7 / 8 log ( 1 - - 1 8 z 8 ) - 7 ( - 1 ) 7 / 8 z 7 / 8 log ( - 1 8 z 8 + 1 ) + 7 ( - 1 ) 5 / 8 z 7 / 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 7 ( - 1 ) 5 / 8 z 7 / 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 7 ( - 1 ) 3 / 8 z 7 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 7 ( - 1 ) 3 / 8 z 7 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 7 - 1 8 z 7 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 7 - 1 8 z 7 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 ) - 2083510 ( - 1 8 ( - ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 3 / 8 z 8 ) + log ( ( - 1 ) 3 / 8 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 7 / 8 z 8 ) + log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 23 / 8 - 8 z 2 7 + 8 z 15 - 8 23 ) - 3854235 ( - 1 8 ( - ( - 1 ) 3 / 4 log ( 1 - - 1 8 z 8 ) + ( - 1 ) 3 / 4 log ( - 1 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 3 / 8 z 8 ) + log ( ( - 1 ) 3 / 8 z 8 + 1 ) - - 1 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + - 1 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 7 / 8 z 8 ) + log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) z 39 / 8 - 8 z 4 7 + 8 z 3 15 - 8 z 2 23 + 8 z 31 - 8 39 ) ) ) HypergeometricPFQ -1 47 8 5 1 8 -1 z 1 68719476736 45742515 435643 -1 1 8 -1 3 4 1 -1 -1 1 8 z 1 8 -1 -1 3 4 -1 1 8 z 1 8 1 1 -1 -1 3 8 z 1 8 -1 -1 3 8 z 1 8 1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 -1 1 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 z 15 8 8 z 7 -1 -1 8 15 4234230 -1 1 8 -1 3 4 1 -1 -1 1 8 z 1 8 -1 -1 3 4 -1 1 8 z 1 8 1 1 -1 -1 3 8 z 1 8 -1 -1 3 8 z 1 8 1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 -1 1 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 z 31 8 8 z 3 7 -1 -1 8 z 2 15 -1 8 z 23 -1 -1 8 31 1295679 -1 1 8 -1 3 4 1 -1 -1 1 8 z 1 8 -1 -1 3 4 -1 1 8 z 1 8 1 1 -1 -1 3 8 z 1 8 -1 -1 3 8 z 1 8 1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 -1 1 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 z 47 8 8 z 5 7 -1 -1 8 z 4 15 -1 8 z 3 23 -1 -1 8 z 2 31 -1 8 z 39 -1 -1 8 47 27807 7 7 -1 7 8 z 7 8 1 -1 -1 1 8 z 1 8 -1 7 -1 7 8 z 7 8 -1 1 8 z 1 8 1 7 -1 5 8 z 7 8 1 -1 -1 3 8 z 1 8 -1 7 -1 5 8 z 7 8 -1 3 8 z 1 8 1 7 -1 3 8 z 7 8 1 -1 -1 5 8 z 1 8 -1 7 -1 3 8 z 7 8 -1 5 8 z 1 8 1 7 -1 1 8 z 7 8 1 -1 -1 7 8 z 1 8 -1 7 -1 1 8 z 7 8 -1 7 8 z 1 8 1 8 -1 2083510 -1 1 8 -1 -1 3 4 1 -1 -1 1 8 z 1 8 -1 3 4 -1 1 8 z 1 8 1 -1 1 -1 -1 3 8 z 1 8 -1 3 8 z 1 8 1 -1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 1 4 -1 5 8 z 1 8 1 -1 1 -1 -1 7 8 z 1 8 -1 7 8 z 1 8 1 z 23 8 -1 8 z 2 7 -1 8 z 15 -1 -1 8 23 -1 3854235 -1 1 8 -1 -1 3 4 1 -1 -1 1 8 z 1 8 -1 3 4 -1 1 8 z 1 8 1 -1 1 -1 -1 3 8 z 1 8 -1 3 8 z 1 8 1 -1 -1 1 4 1 -1 -1 5 8 z 1 8 -1 1 4 -1 5 8 z 1 8 1 -1 1 -1 -1 7 8 z 1 8 -1 7 8 z 1 8 1 z 39 8 -1 8 z 4 7 -1 8 z 3 15 -1 -1 8 z 2 23 -1 8 z 31 -1 -1 8 39 [/itex]

 Rule Form

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

 2007-05-02