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 AiryBi

 http://functions.wolfram.com/03.06.06.0039.01

 Input Form

 AiryBi[z] \[Proportional] ((E^((2 z^(3/2))/3) Sqrt[Pi])/(Sqrt[Pi] z^(1/4))) (Sum[((Pochhammer[1/12, k] Pochhammer[7/12, k] Pochhammer[5/12, k] Pochhammer[11/12, k])/(Pochhammer[1/2, k] k!)) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 (n + 1))]) + ((5 E^((2 z^(3/2))/3))/(48 Sqrt[Pi] z^(7/4))) (Sum[((Pochhammer[7/12, k] Pochhammer[13/12, k] Pochhammer[11/12, k] Pochhammer[17/12, k])/(Pochhammer[3/2, k] k!)) (9/(4 z^3))^k, {k, 0, n}] + O[1/z^(3 (n + 1))]) /; Abs[Arg[z]] < Pi && (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["AiryBi", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], " ", SqrtBox["\[Pi]"]]], RowBox[List[SqrtBox["\[Pi]"], SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["Sum", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "12"], ",", " ", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["7", "12"], ",", " ", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "12"], ",", "k"]], "]"]], RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["11", "12"], ",", "k"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], RowBox[List["k", "!"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], ",", RowBox[List["{", RowBox[List["k", ",", "0", ",", "n"]], "}"]]]], "]"]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List["3", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["5", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]], RowBox[List["48", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["Sum", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["7", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["13", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["11", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["17", "12"], ",", "k"]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], RowBox[List["k", "!"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], ",", RowBox[List["{", RowBox[List["k", ",", "0", ",", "n"]], "}"]]]], "]"]], "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List["3", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]], "]"]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 Bi ( z ) 5 2 z 3 / 2 3 48 π z 7 / 4 ( k = 0 n ( 7 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["7", "12"], ")"]], "k"], Pochhammer] ( 13 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["13", "12"], ")"]], "k"], Pochhammer] ( 11 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["11", "12"], ")"]], "k"], Pochhammer] ( 17 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["17", "12"], ")"]], "k"], Pochhammer] ( 9 4 z 3 ) k ( 3 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], "k"], Pochhammer] k ! + O ( 1 z 3 ( n + 1 ) ) ) + 2 z 3 / 2 3 π z 4 ( k = 0 n ( ( 1 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "12"], ")"]], "k"], Pochhammer] ( 7 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["7", "12"], ")"]], "k"], Pochhammer] ( 5 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["5", "12"], ")"]], "k"], Pochhammer] ( 11 12 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["11", "12"], ")"]], "k"], Pochhammer] ) ( 9 4 z 3 ) k ( 1 2 ) k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], "k"], Pochhammer] k ! + O ( 1 z 3 ( n + 1 ) ) ) /; "\[LeftBracketingBar]" arg ( z ) "\[RightBracketingBar]" < π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] Condition Proportional AiryBi z 5 2 z 3 2 3 -1 48 1 2 z 7 4 -1 k 0 n Pochhammer 7 12 k Pochhammer 13 12 k Pochhammer 11 12 k Pochhammer 17 12 k 9 4 z 3 -1 k Pochhammer 3 2 k k -1 O 1 z 3 n 1 -1 2 z 3 2 3 -1 1 2 z 1 4 -1 k 0 n Pochhammer 1 12 k Pochhammer 7 12 k Pochhammer 5 12 k Pochhammer 11 12 k 9 4 z 3 -1 k Pochhammer 1 2 k k -1 O 1 z 3 n 1 -1 z Rule z n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["AiryBi", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["7", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["5", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["11", "12"], ",", "k"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", "k"]], "]"]], " ", RowBox[List["k", "!"]]]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List["3", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]], "]"]]]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["5", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]]], "3"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "n"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["7", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["13", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["11", "12"], ",", "k"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["17", "12"], ",", "k"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["9", RowBox[List["4", " ", SuperscriptBox["z", "3"]]]], ")"]], "k"]]], RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["3", "2"], ",", "k"]], "]"]], " ", RowBox[List["k", "!"]]]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List["3", " ", RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]]]]]], "]"]]]], ")"]]]], RowBox[List["48", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "4"]]]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", "z", "]"]], "]"]], "<", "\[Pi]"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2007-05-02