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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function





http://functions.wolfram.com/03.09.21.0007.01









  


  










Input Form





Integrate[z^n StruveH[\[Nu], a z], z] == 2^(-2 - \[Nu]) a z^(2 + n) (a z)^\[Nu] Gamma[(1/2) (2 + n + \[Nu])] HypergeometricPFQRegularized[ {1, (1/2) (2 + n + \[Nu])}, {3/2 + \[Nu], 3/2, (1/2) (4 + n + \[Nu])}, (-(1/4)) a^2 z^2]










Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mi> &#957; </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ; </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[OverscriptBox[&quot;F&quot;, &quot;~&quot;], FormBox[&quot;3&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[&quot;1&quot;, HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;2&quot;], &quot; &quot;, RowBox[List[&quot;(&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;\[Nu]&quot;, &quot;+&quot;, &quot;2&quot;]], &quot;)&quot;]]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[RowBox[List[TagBox[RowBox[List[&quot;\[Nu]&quot;, &quot;+&quot;, FractionBox[&quot;3&quot;, &quot;2&quot;]]], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], HypergeometricPFQRegularized, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[FractionBox[&quot;1&quot;, &quot;2&quot;], &quot; 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</ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <ci> a </ci> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> <ci> &#957; </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> n </ci> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <ci> HypergeometricPFQRegularized </ci> <list> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> n </ci> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> </list> <list> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='rational'> 3 <sep /> 2 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> n </ci> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> </list> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





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