html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 BesselY

 http://functions.wolfram.com/03.03.26.0111.01

 Input Form

 BesselY[\[Nu], z] Hypergeometric0F1[\[Nu], -(z^2/4)] == -((2^\[Nu] Csc[\[Nu] Pi])/(z^\[Nu] Gamma[1 - \[Nu]])) + ((2^(-1 + \[Nu]) Gamma[\[Nu]])/Sqrt[Pi]) MeijerG[{{1 - \[Nu]/2}, {(1 - \[Nu])/2}}, {{1 - \[Nu]/2, \[Nu]/2}, {1 - (3 \[Nu])/2, -(\[Nu]/2)}}, z^2] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], RowBox[List["Hypergeometric0F1", "[", RowBox[List["\[Nu]", ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]]]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", "\[Nu]"], SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]]]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]], " "]], SqrtBox["\[Pi]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]]]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]

 MathML Form

 Y ν ( z ) 0 F 1 ( ; ν ; - z 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "0"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox["\[Nu]", Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric0F1, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], Hypergeometric0F1, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], Hypergeometric0F1] 2 ν - 1 Γ ( ν ) π G 2 , 4 2 , 1 ( z 2 1 - ν 2 , 1 - ν 2 1 - ν 2 , ν 2 , 1 - 3 ν 2 , - ν 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "4"]], RowBox[List["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[SuperscriptBox["z", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["\[Nu]", "2"], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["\[Nu]", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] - 2 ν z - ν csc ( ν π ) Γ ( 1 - ν ) /; - π 2 < arg ( z ) π 2 Condition BesselY ν z Hypergeometric0F1 ν -1 z 2 4 -1 2 ν -1 Gamma ν 1 2 -1 MeijerG 1 -1 ν 2 -1 1 -1 ν 2 -1 1 -1 ν 2 -1 ν 2 -1 1 -1 3 ν 2 -1 -1 ν 2 -1 z 2 -1 2 ν z -1 ν ν Gamma 1 -1 ν -1 Inequality -1 2 -1 z 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], " ", RowBox[List["Hypergeometric0F1", "[", RowBox[List["\[Nu]_", ",", RowBox[List["-", FractionBox[SuperscriptBox["z_", "2"], "4"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]]], " ", RowBox[List["Gamma", "[", "\[Nu]", "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]]]], "}"]], ",", SuperscriptBox["z", "2"]]], "]"]]]], SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]

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

 2007-05-02