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

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec

Revision as of 14:40, 2 January 2020

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DLMF:11.4.E18
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    Statements

    Defining formula
    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),}}
    0 references
    DLMF id
    DLMF:11.4.E18
    0 references
    constraint
    ν ≠ - 1 , - 2 , - 3 , … 𝜈 1 2 3 … {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
     
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