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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bxx1.01

 Input Form

 Hypergeometric2F1[1/8, 4, 25/8, z] == (1/1048576) (51 (-(1024/(-1 + z)) - (1/z^(1/8)) (2415 (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)])) - (1/z^(9/8)) (210 (8 z^(1/8) + 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)])) - (1/z^(17/8)) (7 (72 z^(1/8) + 8 z^(9/8) + 9 Log[1 - z^(1/8)] - 9 I Log[1 - I z^(1/8)] + 9 I Log[1 + I z^(1/8)] - 9 Log[1 + z^(1/8)] - 9 (-1)^(3/4) Log[1 - (-1)^(1/4) z^(1/8)] + 9 (-1)^(3/4) Log[1 + (-1)^(1/4) z^(1/8)] - 9 (-1)^(1/4) Log[1 - (-1)^(3/4) z^(1/8)] + 9 (-1)^(1/4) Log[1 + (-1)^(3/4) z^(1/8)]))))

 Standard Form

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 MathML Form

 2 F 1 ( 1 8 , 4 ; 25 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["1", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["4", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["25", "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] 1 1048576 ( 51 ( - 1 z 8 ( 2415 ( 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 ) ) ) - 1 z 9 / 8 ( 210 ( 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 ) + 8 z 8 ) ) - 1 z 17 / 8 ( 7 ( 8 z 9 / 8 + 72 z 8 + 9 log ( 1 - z 8 ) - 9 log ( 1 - z 8 ) + 9 log ( z 8 + 1 ) - 9 log ( z 8 + 1 ) - 9 ( - 1 ) 3 / 4 log ( 1 - - 1 4 z 8 ) + 9 ( - 1 ) 3 / 4 log ( - 1 4 z 8 + 1 ) - 9 - 1 4 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 9 - 1 4 log ( ( - 1 ) 3 / 4 z 8 + 1 ) ) ) - 1024 z - 1 ) ) HypergeometricPFQ 1 8 4 25 8 z 1 1048576 51 -1 1 z 1 8 -1 2415 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -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 -1 1 z 9 8 -1 210 1 -1 z 1 8 -1 1 -1 z 1 8 z 1 8 1 -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 8 z 1 8 -1 1 z 17 8 -1 7 8 z 9 8 72 z 1 8 9 1 -1 z 1 8 -1 9 1 -1 z 1 8 9 z 1 8 1 -1 9 z 1 8 1 -1 9 -1 3 4 1 -1 -1 1 4 z 1 8 9 -1 3 4 -1 1 4 z 1 8 1 -1 9 -1 1 4 1 -1 -1 3 4 z 1 8 9 -1 1 4 -1 3 4 z 1 8 1 -1 1024 z -1 -1 [/itex]

 Rule Form

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

 2007-05-02