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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z1,z2,a,b] > Representations through more general functions > Through Meijer G > Classical cases for the direct function itself





http://functions.wolfram.com/06.20.26.0007.01









  


  








Input Form





Beta[Subscript[z, 1], Subscript[z, 2], a, b] == (1/Gamma[1 - b]) (Subscript[z, 2]^a MeijerG[{{1 - a, b}, {}}, {{0}, {-a}}, -Subscript[z, 2]] - Subscript[z, 1]^a MeijerG[{{1 - a, b}, {}}, {{0}, {-a}}, -Subscript[z, 1]])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"], ",", "a", ",", "b"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]]], RowBox[List["(", RowBox[List[RowBox[List[SubsuperscriptBox["z", "2", "a"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", "b"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "a"]], "}"]]]], "}"]], ",", RowBox[List["-", SubscriptBox["z", "2"]]]]], "]"]]]], "-", RowBox[List[SubsuperscriptBox["z", "1", "a"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", "b"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "a"]], "}"]]]], "}"]], ",", RowBox[List["-", SubscriptBox["z", "1"]]]]], "]"]]]]]], ")"]]]]]]]]








MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SubsuperscriptBox["zz", "2", "a"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", "b"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "a"]], "}"]]]], "}"]], ",", RowBox[List["-", SubscriptBox["zz", "2"]]]]], "]"]]]], "-", RowBox[List[SubsuperscriptBox["zz", "1", "a"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "a"]], ",", "b"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["-", "a"]], "}"]]]], "}"]], ",", RowBox[List["-", SubscriptBox["zz", "1"]]]]], "]"]]]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "b"]], "]"]]]]]]]


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





2001-10-29