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; }

 StruveH

 http://functions.wolfram.com/03.09.06.0053.01

 Input Form

 StruveH[\[Nu], z] \[Proportional] ((-1)^(1 + \[Nu])/Sqrt[-2 Pi z]) (Exp[(-I) z - ((2 \[Nu] + 3)/4) Pi I] (1 - (I (-1 + 4 \[Nu]^2))/(8 z) - (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis]) + Exp[I z + ((2 \[Nu] + 3)/4) Pi I] (1 + (I (-1 + 4 \[Nu]^2))/(8 z) - (9 - 40 \[Nu]^2 + 16 \[Nu]^4)/(128 z^2) + \[Ellipsis])) + ((2^(1 - \[Nu]) (-1)^(1 + \[Nu]) (-z)^(\[Nu] - 1))/ (Sqrt[Pi] Gamma[1/2 + \[Nu]])) (1 + (-1 + 2 \[Nu])/z^2 + (3 (3 - 8 \[Nu] + 4 \[Nu]^2))/z^4 + \[Ellipsis]) /; Inequality[0, Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " "]], SqrtBox[RowBox[List[RowBox[List["-", "2"]], "\[Pi]", " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "-", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[RowBox[List["Exp", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["2", "\[Nu]"]], "+", "3"]], "4"], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]], "]"]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]]]], RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]], RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], SuperscriptBox["z", "4"]], "+", "\[Ellipsis]"]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

 MathML Form

 H StruveH ν ( z ) ( - 1 ) 1 + ν - 2 π z ( z + 1 4 ( 2 ν + 3 ) π ( 1 + ( 4 ν 2 - 1 ) 8 z - 16 ν 4 - 40 ν 2 + 9 128 z 2 + ) + - z - 1 4 ( 2 ν + 3 ) π ( 1 - ( 4 ν 2 - 1 ) 8 z - 16 ν 4 - 40 ν 2 + 9 128 z 2 + ) ) + 2 1 - ν ( - 1 ) ν + 1 ( - z ) ν - 1 π Γ ( ν + 1 2 ) ( 1 + 2 ν - 1 z 2 + 3 ( 4 ν 2 - 8 ν + 3 ) z 4 + ) /; 0 < arg ( z ) π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional StruveH ν z -1 1 ν -2 z 1 2 -1 z 1 4 2 ν 3 1 4 ν 2 -1 8 z -1 -1 16 ν 4 -1 40 ν 2 9 128 z 2 -1 -1 z -1 1 4 2 ν 3 1 -1 4 ν 2 -1 8 z -1 -1 16 ν 4 -1 40 ν 2 9 128 z 2 -1 2 1 -1 ν -1 ν 1 -1 z ν -1 1 2 Gamma ν 1 2 -1 1 2 ν -1 z 2 -1 3 4 ν 2 -1 8 ν 3 z 4 -1 Inequality 0 z Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "-", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], "+", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], RowBox[List["8", " ", "z"]]], "-", FractionBox[RowBox[List["9", "-", RowBox[List["40", " ", SuperscriptBox["\[Nu]", "2"]]], "+", RowBox[List["16", " ", SuperscriptBox["\[Nu]", "4"]]]]], RowBox[List["128", " ", SuperscriptBox["z", "2"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["-", "2"]], " ", "\[Pi]", " ", "z"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "+", "\[Nu]"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "z"]], ")"]], RowBox[List["\[Nu]", "-", "1"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "\[Nu]"]]]], SuperscriptBox["z", "2"]], "+", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["8", " ", "\[Nu]"]], "+", RowBox[List["4", " ", SuperscriptBox["\[Nu]", "2"]]]]], ")"]]]], SuperscriptBox["z", "4"]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.