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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.byo1.01

 Input Form

 Hypergeometric2F1[3/8, 1, 35/8, z] == (1/(8192 z^(27/8))) (9 (-1)^(1/4) (-1672 (-1)^(3/4) z^(3/8) + 4560 (-1)^(3/4) z^(11/8) - 3912 (-1)^(3/4) z^(19/8) + 627 (-1)^(3/4) (-1 + z)^3 Log[1 - z^(1/8)] - 627 (-1)^(1/4) (-1 + z)^3 Log[1 - I z^(1/8)] - 627 (-1)^(1/4) Log[1 + I z^(1/8)] + 1881 (-1)^(1/4) z Log[1 + I z^(1/8)] - 1881 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 627 (-1)^(1/4) z^3 Log[1 + I z^(1/8)] + 627 (-1)^(3/4) Log[1 + z^(1/8)] - 1881 (-1)^(3/4) z Log[1 + z^(1/8)] + 1881 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 627 (-1)^(3/4) z^3 Log[1 + z^(1/8)] - 627 Log[1 - (-1)^(1/4) z^(1/8)] + 1881 z Log[1 - (-1)^(1/4) z^(1/8)] - 1881 z^2 Log[1 - (-1)^(1/4) z^(1/8)] + 627 z^3 Log[1 - (-1)^(1/4) z^(1/8)] + 627 Log[1 + (-1)^(1/4) z^(1/8)] - 1881 z Log[1 + (-1)^(1/4) z^(1/8)] + 1881 z^2 Log[1 + (-1)^(1/4) z^(1/8)] - 627 z^3 Log[1 + (-1)^(1/4) z^(1/8)] - 627 I Log[1 - (-1)^(3/4) z^(1/8)] + 1881 I z Log[1 - (-1)^(3/4) z^(1/8)] - 1881 I z^2 Log[1 - (-1)^(3/4) z^(1/8)] + 627 I z^3 Log[1 - (-1)^(3/4) z^(1/8)] + 627 I Log[1 + (-1)^(3/4) z^(1/8)] - 1881 I z Log[1 + (-1)^(3/4) z^(1/8)] + 1881 I z^2 Log[1 + (-1)^(3/4) z^(1/8)] - 627 I z^3 Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 1 ; 35 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["3", "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["35", "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 8192 z 27 / 8 ( 9 - 1 4 ( 627 ( - 1 ) 3 / 4 log ( 1 - z 8 ) ( z - 1 ) 3 - 627 - 1 4 log ( 1 - z 8 ) ( z - 1 ) 3 - 3912 ( - 1 ) 3 / 4 z 19 / 8 + 4560 ( - 1 ) 3 / 4 z 11 / 8 + 627 - 1 4 z 3 log ( z 8 + 1 ) - 1881 - 1 4 z 2 log ( z 8 + 1 ) + 1881 - 1 4 z log ( z 8 + 1 ) - 627 - 1 4 log ( z 8 + 1 ) - 627 ( - 1 ) 3 / 4 z 3 log ( z 8 + 1 ) + 1881 ( - 1 ) 3 / 4 z 2 log ( z 8 + 1 ) - 1881 ( - 1 ) 3 / 4 z log ( z 8 + 1 ) + 627 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 627 z 3 log ( 1 - - 1 4 z 8 ) - 1881 z 2 log ( 1 - - 1 4 z 8 ) + 1881 z log ( 1 - - 1 4 z 8 ) - 627 log ( 1 - - 1 4 z 8 ) - 627 z 3 log ( - 1 4 z 8 + 1 ) + 1881 z 2 log ( - 1 4 z 8 + 1 ) - 1881 z log ( - 1 4 z 8 + 1 ) + 627 log ( - 1 4 z 8 + 1 ) + 627 z 3 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 1881 z 2 log ( 1 - ( - 1 ) 3 / 4 z 8 ) + 1881 z log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 627 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 627 z 3 log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 1881 z 2 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 1881 z log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 627 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 1672 ( - 1 ) 3 / 4 z 3 / 8 ) ) HypergeometricPFQ 3 8 1 35 8 z 1 8192 z 27 8 -1 9 -1 1 4 627 -1 3 4 1 -1 z 1 8 z -1 3 -1 627 -1 1 4 1 -1 z 1 8 z -1 3 -1 3912 -1 3 4 z 19 8 4560 -1 3 4 z 11 8 627 -1 1 4 z 3 z 1 8 1 -1 1881 -1 1 4 z 2 z 1 8 1 1881 -1 1 4 z z 1 8 1 -1 627 -1 1 4 z 1 8 1 -1 627 -1 3 4 z 3 z 1 8 1 1881 -1 3 4 z 2 z 1 8 1 -1 1881 -1 3 4 z z 1 8 1 627 -1 3 4 z 1 8 1 627 z 3 1 -1 -1 1 4 z 1 8 -1 1881 z 2 1 -1 -1 1 4 z 1 8 1881 z 1 -1 -1 1 4 z 1 8 -1 627 1 -1 -1 1 4 z 1 8 -1 627 z 3 -1 1 4 z 1 8 1 1881 z 2 -1 1 4 z 1 8 1 -1 1881 z -1 1 4 z 1 8 1 627 -1 1 4 z 1 8 1 627 z 3 1 -1 -1 3 4 z 1 8 -1 1881 z 2 1 -1 -1 3 4 z 1 8 1881 z 1 -1 -1 3 4 z 1 8 -1 627 1 -1 -1 3 4 z 1 8 -1 627 z 3 -1 3 4 z 1 8 1 1881 z 2 -1 3 4 z 1 8 1 -1 1881 z -1 3 4 z 1 8 1 627 -1 3 4 z 1 8 1 -1 1672 -1 3 4 z 3 8 [/itex]

 Rule Form

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

 2007-05-02