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 Log

 http://functions.wolfram.com/01.04.20.0007.01

 Input Form

 D[Log[1 + z], {z, \[Alpha]}] == z^(1 - \[Alpha]) Hypergeometric2F1Regularized[1, 1, 2 - \[Alpha], -z]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "\[Alpha]"]], "}"]]], RowBox[List["Log", "[", RowBox[List["1", "+", "z"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "1", ",", RowBox[List["2", "-", "\[Alpha]"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]]

 MathML Form

 α log ( 1 + z ) z α z 1 - α 2 F ~ 1 ( 1 , 1 ; 2 - α ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox["1", Hypergeometric2F1Regularized, Rule[Editable, True]], ",", TagBox["1", Hypergeometric2F1Regularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["2", "-", "\[Alpha]"]], Hypergeometric2F1Regularized, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1Regularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1Regularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1Regularized] z α 1 z z 1 -1 α Hypergeometric2F1Regularized 1 1 2 -1 α -1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "\[Alpha]_"]], "}"]]]]], RowBox[List["Log", "[", RowBox[List["1", "+", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List["1", "-", "\[Alpha]"]]], " ", RowBox[List["Hypergeometric2F1Regularized", "[", RowBox[List["1", ",", "1", ",", RowBox[List["2", "-", "\[Alpha]"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]]]]

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

 2001-10-29