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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Representations through more general functions > Through Meijer G > Classical cases involving sqrt in the arguments





http://functions.wolfram.com/01.02.26.0020.01









  


  








Input Form





(Sqrt[1 + z] + Sqrt[z])^\[Beta]/Sqrt[1 + z] == (1/Sqrt[Pi]) MeijerG[{{(1 + \[Beta])/2}, {(1 - \[Beta])/2}}, {{0, 1/2}, {}}, z] /; !IntervalMemberQ[Interval[{-1, 0}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], "+", SqrtBox["z"]]], ")"]], "\[Beta]"], SqrtBox[RowBox[List["1", "+", "z"]]]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["\[Pi]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Beta]"]], "2"], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Beta]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z_"]]], "+", SqrtBox["z_"]]], ")"]], "\[Beta]_"], SqrtBox[RowBox[List["1", "+", "z_"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["1", "+", "\[Beta]"]], "2"], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Beta]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], SqrtBox["\[Pi]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29