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 Hypergeometric2F1

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

 Input Form

 Hypergeometric2F1[3/8, 1, 19/8, z] == (1/(64 z^(11/8))) (11 (-1)^(1/4) (-8 (-1)^(3/4) z^(3/8) + 3 (-1)^(3/4) (-1 + z) Log[1 - z^(1/8)] - 3 (-1)^(1/4) (-1 + z) Log[1 - I z^(1/8)] - 3 (-1)^(1/4) Log[1 + I z^(1/8)] + 3 (-1)^(1/4) z Log[1 + I z^(1/8)] + 3 (-1)^(3/4) Log[1 + z^(1/8)] - 3 (-1)^(3/4) z Log[1 + z^(1/8)] - 3 Log[1 - (-1)^(1/4) z^(1/8)] + 3 z Log[1 - (-1)^(1/4) z^(1/8)] + 3 Log[1 + (-1)^(1/4) z^(1/8)] - 3 z Log[1 + (-1)^(1/4) z^(1/8)] - 3 I Log[1 - (-1)^(3/4) z^(1/8)] + 3 I z Log[1 - (-1)^(3/4) z^(1/8)] + 3 I Log[1 + (-1)^(3/4) z^(1/8)] - 3 I z Log[1 + (-1)^(3/4) z^(1/8)]))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 1 ; 19 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["19", "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 64 z 11 / 8 ( 11 - 1 4 ( 3 ( - 1 ) 3 / 4 ( z - 1 ) log ( 1 - z 8 ) - 3 - 1 4 ( z - 1 ) log ( 1 - z 8 ) + 3 - 1 4 z log ( z 8 + 1 ) - 3 - 1 4 log ( z 8 + 1 ) - 3 ( - 1 ) 3 / 4 z log ( z 8 + 1 ) + 3 ( - 1 ) 3 / 4 log ( z 8 + 1 ) + 3 z log ( 1 - - 1 4 z 8 ) - 3 log ( 1 - - 1 4 z 8 ) - 3 z log ( - 1 4 z 8 + 1 ) + 3 log ( - 1 4 z 8 + 1 ) + 3 z log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 3 log ( 1 - ( - 1 ) 3 / 4 z 8 ) - 3 z log ( ( - 1 ) 3 / 4 z 8 + 1 ) + 3 log ( ( - 1 ) 3 / 4 z 8 + 1 ) - 8 ( - 1 ) 3 / 4 z 3 / 8 ) ) HypergeometricPFQ 3 8 1 19 8 z 1 64 z 11 8 -1 11 -1 1 4 3 -1 3 4 z -1 1 -1 z 1 8 -1 3 -1 1 4 z -1 1 -1 z 1 8 3 -1 1 4 z z 1 8 1 -1 3 -1 1 4 z 1 8 1 -1 3 -1 3 4 z z 1 8 1 3 -1 3 4 z 1 8 1 3 z 1 -1 -1 1 4 z 1 8 -1 3 1 -1 -1 1 4 z 1 8 -1 3 z -1 1 4 z 1 8 1 3 -1 1 4 z 1 8 1 3 z 1 -1 -1 3 4 z 1 8 -1 3 1 -1 -1 3 4 z 1 8 -1 3 z -1 3 4 z 1 8 1 3 -1 3 4 z 1 8 1 -1 8 -1 3 4 z 3 8 [/itex]

 Rule Form

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

 2007-05-02