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Power






Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Representations through more general functions > Through Meijer G > Generalized cases involving sqrt in the arguments and unit step theta





http://functions.wolfram.com/01.02.26.0044.01









  


  










Input Form





(UnitStep[1 - Abs[z]]/Sqrt[1 - z^2]) ((Sqrt[1 + z] + Sqrt[1 - z])^\[Beta] + (Sqrt[1 + z] - Sqrt[1 - z])^\[Beta]) == 2^(\[Beta]/2 + 1) Sqrt[Pi] MeijerG[{{}, {\[Beta]/4, (\[Beta] + 2)/4}}, {{0, \[Beta]/2}, {}}, z, 1/2] /; !IntervalMemberQ[Interval[{-1, 0}], z]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[FractionBox[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z", "2"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], "+", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], "\[Beta]"], "+", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z"]]], "-", SqrtBox[RowBox[List["1", "-", "z"]]]]], ")"]], "\[Beta]"]]], ")"]]]], "\[Equal]", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["\[Beta]", "2"], "+", "1"]]], SqrtBox["\[Pi]"], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["\[Beta]", "4"], ",", FractionBox[RowBox[List["\[Beta]", "+", "2"]], "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["\[Beta]", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]], "/;", 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[RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z_"]]], "+", SqrtBox[RowBox[List["1", "-", "z_"]]]]], ")"]], "\[Beta]_"], "+", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["1", "+", "z_"]]], "-", SqrtBox[RowBox[List["1", "-", "z_"]]]]], ")"]], "\[Beta]_"]]], ")"]]]], SqrtBox[RowBox[List["1", "-", SuperscriptBox["z_", "2"]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["\[Beta]", "2"], "+", "1"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["\[Beta]", "4"], ",", FractionBox[RowBox[List["\[Beta]", "+", "2"]], "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["\[Beta]", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], "/;", 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





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