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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 hypergeometric functions > Involving 2F1





http://functions.wolfram.com/06.20.26.0005.01









  


  








Input Form





Beta[Subscript[z, 1], Subscript[z, 2], a, b] == (1/b) ((1 - Subscript[z, 1])^b Subscript[z, 1]^a HypergeometricPFQ[{1, a + b}, {1 + b}, 1 - Subscript[z, 1]] - (1 - Subscript[z, 2])^b Subscript[z, 2]^a HypergeometricPFQ[{1, a + b}, {1 + b}, 1 - Subscript[z, 2]]) /; !(Element[-b, Integers] && -b >= 0)








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[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"], ",", "a_", ",", "b_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "1"]]], ")"]], "b"], " ", SubsuperscriptBox["zz", "1", "a"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["a", "+", "b"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "b"]], "}"]], ",", RowBox[List["1", "-", SubscriptBox["zz", "1"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "2"]]], ")"]], "b"], " ", SubsuperscriptBox["zz", "2", "a"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", RowBox[List["a", "+", "b"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "b"]], "}"]], ",", RowBox[List["1", "-", SubscriptBox["zz", "2"]]]]], "]"]]]]]], "b"], "/;", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["-", "b"]], "\[GreaterEqual]", "0"]]]], ")"]]]]]]]]]]


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





2001-10-29