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AppellF1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > AppellF1[a,b1,b2,c,z1,z2] > Series representations > Generalized power series > Expansions at z2==1 > For the function itself





http://functions.wolfram.com/07.36.06.0014.02









  


  










Input Form





AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1], Subscript[z, 2]] \[Proportional] ((Gamma[c] Gamma[c - a - Subscript[b, 2]])/(Gamma[c - a] Gamma[c - Subscript[b, 2]])) Hypergeometric2F1[a, Subscript[b, 1], c - Subscript[b, 2], Subscript[z, 1]] (1 + O[Subscript[z, 2] - 1]) + ((Gamma[c] Gamma[a + Subscript[b, 2] - c])/ ((1 - Subscript[z, 1])^Subscript[b, 1] (Gamma[a] Gamma[Subscript[b, 2]]))) (1 - Subscript[z, 2])^ (c - a - Subscript[b, 2]) (1 + O[Subscript[z, 2] - 1])










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AppellF1", "[", RowBox[List["a_", ",", SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"], ",", "c_", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", "a", "-", SubscriptBox["bb", "2"]]], "]"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", SubscriptBox["bb", "1"], ",", RowBox[List["c", "-", SubscriptBox["bb", "2"]]], ",", SubscriptBox["zz", "1"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List[SubscriptBox["zz", "2"], "-", "1"]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["c", "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["c", "-", SubscriptBox["bb", "2"]]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", "c", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", SubscriptBox["bb", "2"], "-", "c"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "1"]]], ")"]], RowBox[List["-", SubscriptBox["bb", "1"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SubscriptBox["zz", "2"]]], ")"]], RowBox[List["c", "-", "a", "-", SubscriptBox["bb", "2"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List[SubscriptBox["zz", "2"], "-", "1"]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["Gamma", "[", "a", "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "2"], "]"]]]]]]]]]]]










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





2001-10-29