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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/8, 2, 27/8, -z] == -((1/(8192 z^(19/8))) (209 (-1)^(1/8) (88 (-1)^(7/8) z^(3/8) + 24 (-1)^(7/8) z^(11/8) - 3 I (-11 - 6 z + 5 z^2) Log[1 - (-1)^(1/8) z^(1/8)] + 3 I (-11 - 6 z + 5 z^2) Log[1 + (-1)^(1/8) z^(1/8)] - 33 (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] + (9 - 9 I) Sqrt[2] z Log[1 - (-1)^(3/8) z^(1/8)] + 15 (-1)^(3/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] + 33 (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + 18 (-1)^(3/4) z Log[1 + (-1)^(3/8) z^(1/8)] - 15 (-1)^(3/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] - 33 Log[1 - (-1)^(5/8) z^(1/8)] - 18 z Log[1 - (-1)^(5/8) z^(1/8)] + 15 z^2 Log[1 - (-1)^(5/8) z^(1/8)] + 33 Log[1 + (-1)^(5/8) z^(1/8)] + 18 z Log[1 + (-1)^(5/8) z^(1/8)] - 15 z^2 Log[1 + (-1)^(5/8) z^(1/8)] + 33 (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + (9 + 9 I) Sqrt[2] z Log[1 - (-1)^(7/8) z^(1/8)] - 15 (-1)^(1/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 33 (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)] - 18 (-1)^(1/4) z Log[1 + (-1)^(7/8) z^(1/8)] + 15 (-1)^(1/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 2 ; 27 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["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["27", "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 8192 z 19 / 8 ( 209 - 1 8 ( 15 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 - 15 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 + 15 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 - 15 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 - 15 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 + 15 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 24 ( - 1 ) 7 / 8 z 11 / 8 + ( 9 - 9 ) 2 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 18 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 18 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 18 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + ( 9 + 9 ) 2 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 18 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 88 ( - 1 ) 7 / 8 z 3 / 8 - 3 ( 5 z 2 - 6 z - 11 ) log ( 1 - - 1 8 z 8 ) + 3 ( 5 z 2 - 6 z - 11 ) log ( - 1 8 z 8 + 1 ) - 33 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 33 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 33 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 33 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 33 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 33 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 3 8 2 27 8 -1 z -1 1 8192 z 19 8 -1 209 -1 1 8 15 -1 3 4 1 -1 -1 3 8 z 1 8 z 2 -1 15 -1 3 4 -1 3 8 z 1 8 1 z 2 15 1 -1 -1 5 8 z 1 8 z 2 -1 15 -1 5 8 z 1 8 1 z 2 -1 15 -1 1 4 1 -1 -1 7 8 z 1 8 z 2 15 -1 1 4 -1 7 8 z 1 8 1 z 2 24 -1 7 8 z 11 8 9 -9 2 1 2 1 -1 -1 3 8 z 1 8 z 18 -1 3 4 -1 3 8 z 1 8 1 z -1 18 1 -1 -1 5 8 z 1 8 z 18 -1 5 8 z 1 8 1 z 9 9 2 1 2 1 -1 -1 7 8 z 1 8 z -1 18 -1 1 4 -1 7 8 z 1 8 1 z 88 -1 7 8 z 3 8 -1 3 5 z 2 -1 6 z -11 1 -1 -1 1 8 z 1 8 3 5 z 2 -1 6 z -11 -1 1 8 z 1 8 1 -1 33 -1 3 4 1 -1 -1 3 8 z 1 8 33 -1 3 4 -1 3 8 z 1 8 1 -1 33 1 -1 -1 5 8 z 1 8 33 -1 5 8 z 1 8 1 33 -1 1 4 1 -1 -1 7 8 z 1 8 -1 33 -1 1 4 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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

 2007-05-02