DLMF:2.8.E26 (Q961): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11069 / rank
 
Normal rank
Property / Symbols used: Q11069 / qualifier
 
Defining formula:

u 𝑢 {\displaystyle{\displaystyle u}}

u
Property / Symbols used: Q11069 / qualifier
 
xml-id: C2.S8.XMD4.m1ndec

Latest revision as of 17:28, 1 January 2020

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DLMF:2.8.E26
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    Statements

    Defining formula
    W n , 2 ⁢ ( u , ξ ) = ξ 1 / 2 ⁢ K ν ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s - ξ ⁢ K ν + 1 ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + 1 + ξ 1 / 2 ⁢ K ν ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ O ⁡ ( 1 u 2 ⁢ n - 1 ) . subscript 𝑊 𝑛 2 𝑢 𝜉 superscript 𝜉 1 2 modified-Bessel-second-kind 𝜈 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 𝜉 modified-Bessel-second-kind 𝜈 1 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 2 subscript 𝐵 𝑠 𝜉 superscript 𝑢 2 𝑠 1 superscript 𝜉 1 2 modified-Bessel-second-kind 𝜈 𝑢 superscript 𝜉 1 2 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,2}(u,\xi)=\xi^{1/2}K_{\nu}\left(u\xi^{1/2}% \right)\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}-\xi K_{\nu+1}\left(u\xi^{1/2}% \right)\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+\xi^{1/2}K_{\nu}\left(u\xi^% {1/2}\right)O\left(\frac{1}{u^{2n-1}}\right).}}
    0 references
    DLMF id
    DLMF:2.8.E26
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2agdec
    0 references
    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
    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.m1bdec
    0 references
    Q11086
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S8.XMD21.m1bdec
    0 references
    Q11087
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD22.m1adec
    0 references
    Q11088
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD23.m1adec
    0 references
    Q11089
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD24.m1adec
    0 references
    Q11069
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1ndec
    0 references
     
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