Struve function H: Representations through equivalent functions (formula 03.09.27.0001)

StruveH

$Mathematica Notation$

Bessel-Type Functions

StruveH[nu,z]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/03.09.27.0001.01

Input Form

StruveH[\[Nu], I z] == (I (I z)^\[Nu] StruveL[\[Nu], z])/z^\[Nu]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "\[Equal]", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]], "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> H </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveH </ci> </annotation-xml> </semantics> </mstyle> <mi> ν </mi> </msub> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> StruveH </ci> <ci> ν </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <ci> ν </ci> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> ν </ci> </apply> </apply> <apply> <ci> StruveL </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", RowBox[List["\[ImaginaryI]", " ", "z_"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]], "\[Nu]"], " ", SuperscriptBox["z", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["StruveL", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]]]]]]

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

2001-10-29