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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==0 > For the function itself





http://functions.wolfram.com/07.36.06.0006.02









  


  










Input Form





AppellF1[a, Subscript[b, 1], Subscript[b, 2], c, Subscript[z, 1], Subscript[z, 2]] \[Proportional] Hypergeometric2F1[a, Subscript[b, 1], c, Subscript[z, 11]] + ((a Subscript[b, 2] Hypergeometric2F1[1 + a, Subscript[b, 1], 1 + c, Subscript[z, 1]])/c) Subscript[z, 2] + ((1/(2 c (1 + c))) (a (1 + a) Subscript[b, 2] (1 + Subscript[b, 2]) Hypergeometric2F1[2 + a, Subscript[b, 1], 2 + c, Subscript[z, 1]])) Subscript[z, 2]^2 + \[Ellipsis] /; (Subscript[z, 2] -> 0)










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[RowBox[List[RowBox[List["Hypergeometric2F1", "[", RowBox[List["a", ",", SubscriptBox["bb", "1"], ",", "c", ",", SubscriptBox["zz", "11"]]], "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", " ", SubscriptBox["bb", "2"], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["1", "+", "a"]], ",", SubscriptBox["bb", "1"], ",", RowBox[List["1", "+", "c"]], ",", SubscriptBox["zz", "1"]]], "]"]]]], ")"]], " ", SubscriptBox["zz", "2"]]], "c"], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", SubscriptBox["bb", "2"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List["2", "+", "a"]], ",", SubscriptBox["bb", "1"], ",", RowBox[List["2", "+", "c"]], ",", SubscriptBox["zz", "1"]]], "]"]]]], ")"]], " ", SubsuperscriptBox["zz", "2", "2"]]], RowBox[List["2", " ", "c", " ", RowBox[List["(", RowBox[List["1", "+", "c"]], ")"]]]]], "+", "\[Ellipsis]"]], "/;", RowBox[List["(", RowBox[List[SubscriptBox["zz", "2"], "\[Rule]", "0"]], ")"]]]]]]]]










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





2001-10-29