DLMF:2.8.E23 (Q958): Difference between revisions

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‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11081 / rank
 
Normal rank
Property / Symbols used: Q11081 / qualifier
 
Defining formula:

Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}

\AiryBi@{\NVar{z}}
Property / Symbols used: Q11081 / qualifier
 
xml-id: C9.S2.SS1.m2addec
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2aedec
Property / Symbols used
 
Property / Symbols used: Q11083 / rank
 
Normal rank
Property / Symbols used: Q11083 / qualifier
 
Defining formula:

envBi ⁡ ( x ) envelope-Airy-Bi 𝑥 {\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}

\envAiryBi@{\NVar{x}}
Property / Symbols used: Q11083 / qualifier
 
xml-id: C2.S8.SS3.p4.m6abdec
Property / Symbols used
 
Property / Symbols used: Q11077 / rank
 
Normal rank
Property / Symbols used: Q11077 / 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: Q11077 / qualifier
 
xml-id: C2.S8.XMD15.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11078 / rank
 
Normal rank
Property / Symbols used: Q11078 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11078 / qualifier
 
xml-id: C2.S8.XMD16.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11079 / rank
 
Normal rank
Property / Symbols used: Q11079 / qualifier
 
Defining formula:

A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}

A_{s}(\xi)
Property / Symbols used: Q11079 / qualifier
 
xml-id: C2.S8.XMD17.m1edec
Property / Symbols used
 
Property / Symbols used: Q11080 / rank
 
Normal rank
Property / Symbols used: Q11080 / qualifier
 
Defining formula:

B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}

B_{s}(\xi)
Property / Symbols used: Q11080 / qualifier
 
xml-id: C2.S8.XMD18.m1edec
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.m1kdec

Latest revision as of 17:28, 1 January 2020

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DLMF:2.8.E23
No description defined

    Statements

    Defining formula
    W n , 2 ⁢ ( u , ξ ) = Bi ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ∑ s = 0 n - 1 A s ⁢ ( ξ ) u 2 ⁢ s + Bi ′ ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ ∑ s = 0 n - 2 B s ⁢ ( ξ ) u 2 ⁢ s + ( 4 / 3 ) + envBi ⁡ ( u 2 / 3 ⁢ ξ ) ⁢ O ⁡ ( 1 u 2 ⁢ n - 1 ) , subscript 𝑊 𝑛 2 𝑢 𝜉 Airy-Bi superscript 𝑢 2 3 𝜉 superscript subscript 𝑠 0 𝑛 1 subscript 𝐴 𝑠 𝜉 superscript 𝑢 2 𝑠 diffop Airy-Bi 1 superscript 𝑢 2 3 𝜉 superscript subscript 𝑠 0 𝑛 2 subscript 𝐵 𝑠 𝜉 superscript 𝑢 2 𝑠 4 3 envelope-Airy-Bi superscript 𝑢 2 3 𝜉 Big-O 1 superscript 𝑢 2 𝑛 1 {\displaystyle{\displaystyle W_{n,2}(u,\xi)=\mathrm{Bi}\left(u^{2/3}\xi\right)% \sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+\mathrm{Bi}'\left(u^{2/3}\xi\right)% \sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+(4/3)}}+\mathrm{envBi}\left(u^{2/3}\xi% \right)O\left(\frac{1}{u^{2n-1}}\right),}}
    0 references
    DLMF id
    DLMF:2.8.E23
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2addec
    0 references
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aedec
    0 references
    Q11083
    Defining formula
    envBi ⁡ ( x ) envelope-Airy-Bi 𝑥 {\displaystyle{\displaystyle\mathrm{envBi}\left(\NVar{x}\right)}}
    xml-id
    C2.S8.SS3.p4.m6abdec
    0 references
    Q11077
    Defining formula
    W n , j ⁢ ( u , ξ ) subscript 𝑊 𝑛 𝑗 𝑢 𝜉 {\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
    xml-id
    C2.S8.XMD15.m1ddec
    0 references
    Q11078
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S8.XMD16.m1cdec
    0 references
    Q11079
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD17.m1edec
    0 references
    Q11080
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD18.m1edec
    0 references
    Q11069
    Defining formula
    u 𝑢 {\displaystyle{\displaystyle u}}
    xml-id
    C2.S8.XMD4.m1kdec
    0 references
     
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