DLMF:2.8.E29 (Q964): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11085 / rank
 
Normal rank
Property / Symbols used: Q11085 / qualifier
 
Defining formula:

W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}

W_{n,j}(u,\xi)
Property / Symbols used: Q11085 / qualifier
 
xml-id: C2.S8.XMD20.m1cdec

Revision as of 17:29, 1 January 2020

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DLMF:2.8.E29
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    Statements

    Defining formula
    W n , 3 ⁢ ( u , ξ ) = | ξ | 1 / 2 ⁢ J ν ⁡ ( u ⁢ | ξ | 1 / 2 ) ⁢ ( ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s + O ⁡ ( 1 u 2 ⁢ n - 1 ) ) - | ξ | ⁢ J ν + 1 ⁡ ( u ⁢ | ξ | 1 / 2 ) ⁢ ( ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + 1 + O ⁡ ( 1 u 2 ⁢ n - 2 ) ) , subscript 𝑊 𝑛 3 𝑢 𝜉 superscript 𝜉 1 2 Bessel-J 𝜈 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 Big-O 1 superscript 𝑢 2 𝑛 1 𝜉 Bessel-J 𝜈 1 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 2 subscript 𝐵 𝑠 𝜉 superscript 𝑢 2 𝑠 1 Big-O 1 superscript 𝑢 2 𝑛 2 {\displaystyle{\displaystyle W_{n,3}(u,\xi)=|\xi|^{1/2}J_{\nu}\left(u|\xi|^{1/% 2}\right)\left(\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+O\left(\frac{1}{u^{2n% -1}}\right)\right)-|\xi|J_{\nu+1}\left(u|\xi|^{1/2}\right)\left(\sum_{s=0}^{n-% 2}\frac{B_{s}(\xi)}{u^{2s+1}}+O\left(\frac{1}{u^{2n-2}}\right)\right),}}
    0 references
    DLMF id
    DLMF:2.8.E29
    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.m2adec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2ahdec
    0 references
    Q11085
    Defining formula
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD20.m1cdec
    0 references
     
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