DLMF:10.21.E15 (Q3299): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1adec

Revision as of 15:41, 2 January 2020

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DLMF:10.21.E15
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    Statements

    Defining formula
    J ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν Γ ⁡ ( ν + 1 ) ⁢ ∏ k = 1 ∞ ( 1 - z 2 j ν , k 2 ) , Bessel-J 𝜈 𝑧 superscript 1 2 𝑧 𝜈 Euler-Gamma 𝜈 1 superscript subscript product 𝑘 1 1 superscript 𝑧 2 zero-Bessel-J 𝜈 𝑘 2 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{(\tfrac{1}{2}z)^{\nu}% }{\Gamma\left(\nu+1\right)}\prod_{k=1}^{\infty}\left(1-\frac{z^{2}}{{j_{\nu,k}% ^{2}}}\right),}}
    0 references
    DLMF id
    DLMF:10.21.E15
    0 references
    constraint
    ν ≥ 0 𝜈 0 {\displaystyle{\displaystyle\nu\geq 0}}
    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.m2adec
    0 references
    Q11456
    Defining formula
    j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}
    xml-id
    C10.S21.SS1.p2.m11aedec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1dec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
     
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