Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Series representations > Asymptotic series expansions > The general formulas





http://functions.wolfram.com/03.09.06.0009.01









  


  










Input Form





StruveH[\[Nu], z] \[Proportional] (z/2)^(\[Nu] + 1) (AsymptoticHypergeometricPFQRegularizedSeries[Power][{1}, {3/2, \[Nu] + 3/2}, {-(z^2/4), ComplexInfinity, Infinity}] + AsymptoticHypergeometricPFQRegularizedSeries[Trig][{1}, {3/2, \[Nu] + 3/2}, {-(z^2/4), ComplexInfinity, Infinity}]) /; (Abs[z] -> Infinity)










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["StruveH", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["\[Nu]", "+", "1"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["AsymptoticHypergeometricPFQRegularizedSeries", "[", "Power", "]"]], "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["\[Nu]", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], ",", "ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "]"]], "+", RowBox[List[RowBox[List["AsymptoticHypergeometricPFQRegularizedSeries", "[", "Trig", "]"]], "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["\[Nu]", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], ",", "ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "]"]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <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> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8733; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msubsup> <mi> &#119964; </mi> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mrow> <mo> ( </mo> <mi> power </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ; </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <msubsup> <mi> &#119964; </mi> <mover> <mi> F </mi> <mo> ~ </mo> </mover> <mrow> <mo> ( </mo> <mi> trig </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mrow> <mtable> <mtr> <mtd> <mrow> <mn> 1 </mn> <mo> ; </mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mrow> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo> &#8290; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mn> 4 </mn> </mfrac> </mrow> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> <mo> , </mo> <mi> &#8734; </mi> </mrow> <mo> } </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <semantics> <mo> &#8594; </mo> <annotation encoding='Mathematica'> &quot;\[Rule]&quot; </annotation> </semantics> <mi> &#8734; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <apply> <ci> InterpretationBox </ci> <ms> H </ms> <ci> StruveH </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> <apply> <ci> Rule </ci> <ci> Selectable </ci> <false /> </apply> </apply> <ms> &#957; </ms> </apply> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> <ms> &#8733; </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> FractionBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#957; </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> &#119964; </ms> <apply> <ci> OverscriptBox </ci> <ms> F </ms> <ms> ~ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> power </ms> <ms> ) </ms> </list> </apply> </apply> <ms> [ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> ; </ms> </list> </apply> </list> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 3 </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#957; </ms> <ms> + </ms> <apply> <ci> FractionBox </ci> <ms> 3 </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </apply> </list> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> { </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> <ms> 4 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> OverscriptBox </ci> <ms> &#8734; </ms> <ms> ~ </ms> </apply> <ms> , </ms> <ms> &#8734; </ms> </list> </apply> <ms> } </ms> </list> </apply> </list> </apply> <ms> ] </ms> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> &#119964; </ms> <apply> <ci> OverscriptBox </ci> <ms> F </ms> <ms> ~ </ms> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> trig </ms> <ms> ) </ms> </list> </apply> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> ; </ms> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <ms> 3 </ms> <ms> 2 </ms> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#957; </ms> <ms> + </ms> <apply> <ci> FractionBox </ci> <ms> 3 </ms> <ms> 2 </ms> </apply> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </list> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> { </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <ms> z </ms> <ms> 2 </ms> </apply> <ms> 4 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> OverscriptBox </ci> <ms> &#8734; </ms> <ms> ~ </ms> </apply> <ms> , </ms> <ms> &#8734; </ms> </list> </apply> <ms> } </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#62979; </ms> <ms> z </ms> <ms> &#62980; </ms> </list> </apply> <ms> &#62754; </ms> <ms> &#8734; </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["StruveH", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["\[Nu]", "+", "1"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["AsymptoticHypergeometricPFQRegularizedSeries", "[", "Power", "]"]], "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["\[Nu]", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], ",", "ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "]"]], "+", RowBox[List[RowBox[List["AsymptoticHypergeometricPFQRegularizedSeries", "[", "Trig", "]"]], "[", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["\[Nu]", "+", FractionBox["3", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["z", "2"], "4"]]], ",", "ComplexInfinity", ",", "\[Infinity]"]], "}"]]]], "]"]]]], ")"]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]










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





2001-10-29