DLMF:11.4.E18 (Q3950): Difference between revisions

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Property / constraint
 

ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}

\nu\neq-1,-2,-3,\dots
Property / constraint: ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}} / rank
 
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Revision as of 17:41, 30 December 2019

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DLMF:11.4.E18
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    𝐇 ν ( z ) = 4 π 1 / 2 Γ ( ν + 1 2 ) k = 0 ( 2 k + ν + 1 ) Γ ( k + ν + 1 ) k ! ( 2 k + 1 ) ( 2 k + 2 ν + 1 ) J 2 k + ν + 1 ( z ) , Struve-H 𝜈 𝑧 4 superscript 𝜋 1 2 Euler-Gamma 𝜈 1 2 superscript subscript 𝑘 0 2 𝑘 𝜈 1 Euler-Gamma 𝑘 𝜈 1 𝑘 2 𝑘 1 2 𝑘 2 𝜈 1 Bessel-J 2 𝑘 𝜈 1 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\frac{4}{\pi^{1/2}% \Gamma\left(\nu+\tfrac{1}{2}\right)}\*\sum_{k=0}^{\infty}\frac{(2k+\nu+1)% \Gamma\left(k+\nu+1\right)}{k!(2k+1)(2k+2\nu+1)}J_{2k+\nu+1}\left(z\right),}}
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    DLMF:11.4.E18
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    ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
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