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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.c0co.01

 Input Form

 Hypergeometric2F1[5/8, 5, 21/8, -z] == (1/6291456) (65 ((64 (1059 + 1558 z + 627 z^2))/(1 + z)^3 + (1/z^(5/8)) (16929 (-1)^(1/8) ((-1)^(1/4) Log[1 - (-1)^(1/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/8) z^(1/8)] - Log[1 - (-1)^(3/8) z^(1/8)] + Log[1 + (-1)^(3/8) z^(1/8)] - (-1)^(3/4) Log[1 - (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 + (-1)^(5/8) z^(1/8)] + I Log[1 - (-1)^(7/8) z^(1/8)] - I Log[1 + (-1)^(7/8) z^(1/8)])) + (1/z^(13/8)) (627 (8 z^(5/8) - 5 (-1)^(3/8) Log[1 - (-1)^(1/8) z^(1/8)] + 5 (-1)^(3/8) Log[1 + (-1)^(1/8) z^(1/8)] + 5 (-1)^(1/8) Log[1 - (-1)^(3/8) z^(1/8)] - 5 (-1)^(1/8) Log[1 + (-1)^(3/8) z^(1/8)] + 5 (-1)^(7/8) Log[1 - (-1)^(5/8) z^(1/8)] - 5 (-1)^(7/8) Log[1 + (-1)^(5/8) z^(1/8)] - 5 (-1)^(5/8) Log[1 - (-1)^(7/8) z^(1/8)] + 5 (-1)^(5/8) Log[1 + (-1)^(7/8) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 5 8 , 5 ; 21 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["5", "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["21", "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 6291456 ( 65 ( 64 ( 627 z 2 + 1558 z + 1059 ) ( z + 1 ) 3 + 1 z 5 / 8 ( 16929 - 1 8 ( - 1 4 log ( 1 - - 1 8 z 8 ) - - 1 4 log ( - 1 8 z 8 + 1 ) - log ( 1 - ( - 1 ) 3 / 8 z 8 ) + log ( ( - 1 ) 3 / 8 z 8 + 1 ) - ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + ( - 1 ) 3 / 4 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + log ( 1 - ( - 1 ) 7 / 8 z 8 ) - log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) + 1 z 13 / 8 ( 627 ( - 5 ( - 1 ) 3 / 8 log ( 1 - - 1 8 z 8 ) + 5 ( - 1 ) 3 / 8 log ( - 1 8 z 8 + 1 ) + 5 - 1 8 log ( 1 - ( - 1 ) 3 / 8 z 8 ) - 5 - 1 8 log ( ( - 1 ) 3 / 8 z 8 + 1 ) + 5 ( - 1 ) 7 / 8 log ( 1 - ( - 1 ) 5 / 8 z 8 ) - 5 ( - 1 ) 7 / 8 log ( ( - 1 ) 5 / 8 z 8 + 1 ) - 5 ( - 1 ) 5 / 8 log ( 1 - ( - 1 ) 7 / 8 z 8 ) + 5 ( - 1 ) 5 / 8 log ( ( - 1 ) 7 / 8 z 8 + 1 ) + 8 z 5 / 8 ) ) ) ) HypergeometricPFQ 5 8 5 21 8 -1 z 1 6291456 65 64 627 z 2 1558 z 1059 z 1 3 -1 1 z 5 8 -1 16929 -1 1 8 -1 1 4 1 -1 -1 1 8 z 1 8 -1 -1 1 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 3 4 1 -1 -1 5 8 z 1 8 -1 3 4 -1 5 8 z 1 8 1 1 -1 -1 7 8 z 1 8 -1 -1 7 8 z 1 8 1 1 z 13 8 -1 627 -5 -1 3 8 1 -1 -1 1 8 z 1 8 5 -1 3 8 -1 1 8 z 1 8 1 5 -1 1 8 1 -1 -1 3 8 z 1 8 -1 5 -1 1 8 -1 3 8 z 1 8 1 5 -1 7 8 1 -1 -1 5 8 z 1 8 -1 5 -1 7 8 -1 5 8 z 1 8 1 -1 5 -1 5 8 1 -1 -1 7 8 z 1 8 5 -1 5 8 -1 7 8 z 1 8 1 8 z 5 8 [/itex]

 Rule Form

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

 2007-05-02