DLMF:2.8.E25 (Q960): Difference between revisions

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‎Changed an Item: Add constraint
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Property / Symbols used
 
Property / Symbols used: Q11087 / rank
 
Normal rank
Property / Symbols used: Q11087 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11087 / qualifier
 
xml-id: C2.S8.XMD22.m1dec

Revision as of 17:28, 1 January 2020

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DLMF:2.8.E25
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    Statements

    Defining formula
    W n , 1 ⁢ ( u , ξ ) = ξ 1 / 2 ⁢ I ν ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s + ξ ⁢ I ν + 1 ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + 1 + ξ 1 / 2 ⁢ I ν ⁡ ( u ⁢ ξ 1 / 2 ) ⁢ O ⁡ ( 1 u 2 ⁢ n - 1 ) , subscript 𝑊 𝑛 1 𝑢 𝜉 superscript 𝜉 1 2 modified-Bessel-first-kind 𝜈 𝑢 superscript 𝜉 1 2 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 𝜉 modified-Bessel-first-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-first-kind 𝜈 𝑢 superscript 𝜉 1 2 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,1}(u,\xi)=\xi^{1/2}I_{\nu}\left(u\xi^{1/2}% \right)\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+\xi I_{\nu+1}\left(u\xi^{1/2}% \right)\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+\xi^{1/2}I_{\nu}\left(u\xi^% {1/2}\right)O\left(\frac{1}{u^{2n-1}}\right),}}
    0 references
    DLMF id
    DLMF:2.8.E25
    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.m2afdec
    0 references
    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.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.m1adec
    0 references
    Q11086
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C2.S8.XMD21.m1adec
    0 references
    Q11087
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD22.m1dec
    0 references
     
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