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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Identities > Recurrence identities > Distant neighbors > Decreasing





http://functions.wolfram.com/03.09.17.0011.01









  


  










Input Form





StruveH[\[Nu], z] == (2^(1 - \[Nu]) z^(-9 + \[Nu]) (40320 - 6840 z^2 + 9 z^4 - z^6 + z^8 - 219168 \[Nu] + 28116 z^2 \[Nu] - 24 z^4 \[Nu] + 2 z^6 \[Nu] + 472496 \[Nu]^2 - 40652 z^2 \[Nu]^2 + 12 z^4 \[Nu]^2 - 538272 \[Nu]^3 + 28200 z^2 \[Nu]^3 + 359184 \[Nu]^4 - 10160 z^2 \[Nu]^4 - 145152 \[Nu]^5 + 1824 z^2 \[Nu]^5 + 34944 \[Nu]^6 - 128 z^2 \[Nu]^6 - 4608 \[Nu]^7 + 256 \[Nu]^8))/(Sqrt[Pi] Gamma[1/2 + \[Nu]]) - (1 - (4 (-2 + \[Nu]) (-1 + \[Nu]))/z^2 + (8 (-4 + \[Nu]) (-2 + \[Nu]) (6 - z^2 - 8 \[Nu] + 2 \[Nu]^2))/z^4) StruveH[-6 + \[Nu], z] + (1/z^5) (2 (-3 + \[Nu]) (3 z^4 - 16 z^2 (8 - 6 \[Nu] + \[Nu]^2) + 16 (40 - 78 \[Nu] + 49 \[Nu]^2 - 12 \[Nu]^3 + \[Nu]^4)) StruveH[-5 + \[Nu], z])










Standard Form





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MathML Form







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</mo> <mi> &#957; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> <mo> + </mo> <mrow> <mn> 12 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 128 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 6 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 1824 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 5 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10160 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28200 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 40652 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 28116 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 6840 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 256 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 8 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4608 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 7 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 34944 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 6 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 145152 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 5 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 359184 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 538272 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 472496 </mn> <mo> &#8290; </mo> <msup> <mi> &#957; </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 219168 </mn> <mo> &#8290; </mo> <mi> &#957; </mi> </mrow> <mo> + </mo> <mn> 40320 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> StruveH </ci> <ci> &#957; </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> StruveH </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -6 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 49 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78 </cn> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 40 </cn> </apply> </apply> </apply> <apply> <ci> StruveH </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -5 </cn> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -9 </cn> </apply> </apply> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <ci> &#957; </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 128 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1824 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10160 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28200 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 40652 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 28116 </cn> <ci> &#957; </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 256 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4608 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 34944 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 145152 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 359184 </cn> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 538272 </cn> <apply> <power /> <ci> &#957; 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Rule Form





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





2002-12-18





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