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variants of this functions
Beta




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Beta[z,a,b] > Continued fraction representations





http://functions.wolfram.com/06.19.10.0001.01









  


  








Input Form





Beta[z, a, b] == ((z^a (1 - z)^b)/a) (1/ (1 + r[1]/(1 + r[2]/(1 + r[3]/(1 + r[4]/(1 + r[5]/(1 + \[Ellipsis]))))))) /; r[2 k + 1] == -(((a + k) (a + b + k) z)/((a + 2 k) (a + 2 k + 1))) && r[2 k] == (k (b - k) z)/((a + 2 k - 1) (a + 2 k))








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Beta", "[", RowBox[List["z_", ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", "a"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], "b"]]], RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["r", "[", "1", "]"]], RowBox[List["1", "+", FractionBox[RowBox[List["r", "[", "2", "]"]], RowBox[List["1", "+", FractionBox[RowBox[List["r", "[", "3", "]"]], RowBox[List["1", "+", FractionBox[RowBox[List["r", "[", "4", "]"]], RowBox[List["1", "+", FractionBox[RowBox[List["r", "[", "5", "]"]], RowBox[List["1", "+", "\[Ellipsis]"]]]]]]]]]]]]]]]]], ")"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["r", "[", RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]], "]"]], "\[Equal]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "k"]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", "k"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "k"]]]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "k"]], "+", "1"]], ")"]]]]]]]]], "&&", RowBox[List[RowBox[List["r", "[", RowBox[List["2", " ", "k"]], "]"]], "\[Equal]", FractionBox[RowBox[List["k", " ", RowBox[List["(", RowBox[List["b", "-", "k"]], ")"]], " ", "z"]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "k"]], "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "k"]]]], ")"]]]]]]]]]]]]]]]


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





2001-10-29