DLMF:2.8.E17 (Q951): Difference between revisions

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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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11071 / rank
 
Normal rank
Property / Symbols used: Q11071 / qualifier
 
Defining formula:

ψ ⁢ ( ξ ) 𝜓 𝜉 {\displaystyle{\displaystyle\psi(\xi)}}

\psi(\xi)
Property / Symbols used: Q11071 / qualifier
 
xml-id: C2.S8.XMD7.m1fdec

Latest revision as of 17:27, 1 January 2020

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DLMF:2.8.E17
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    Statements

    Defining formula
    B s ⁢ ( ξ ) = { 1 2 ⁢ ξ 1 / 2 ⁢ ∫ 0 ξ ( ψ ⁢ ( v ) ⁢ A s ⁢ ( v ) - A s ′′ ⁢ ( v ) ) ⁢ d v v 1 / 2 , ξ > 0 , 1 2 ⁢ ( - ξ ) 1 / 2 ⁢ ∫ ξ 0 ( ψ ⁢ ( v ) ⁢ A s ⁢ ( v ) - A s ′′ ⁢ ( v ) ) ⁢ d v ( - v ) 1 / 2 , ξ < 0 , subscript 𝐵 𝑠 𝜉 cases 1 2 superscript 𝜉 1 2 superscript subscript 0 𝜉 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 superscript subscript 𝐴 𝑠 ′′ 𝑣 𝑣 superscript 𝑣 1 2 𝜉 0 1 2 superscript 𝜉 1 2 superscript subscript 𝜉 0 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 superscript subscript 𝐴 𝑠 ′′ 𝑣 𝑣 superscript 𝑣 1 2 𝜉 0 {\displaystyle{\displaystyle B_{s}(\xi)=\begin{cases}\dfrac{1}{2\xi^{1/2}}% \displaystyle\int_{0}^{\xi}\left(\psi(v)A_{s}(v)-A_{s}^{\prime\prime}(v)\right% )\dfrac{\mathrm{d}v}{v^{1/2}},&\xi>0,\\ \dfrac{1}{2(-\xi)^{1/2}}\displaystyle\int_{\xi}^{0}\left(\psi(v)A_{s}(v)-A_{s}% ^{\prime\prime}(v)\right)\dfrac{\mathrm{d}v}{(-v)^{1/2}},&\xi<0,\end{cases}}}
    0 references
    DLMF id
    DLMF:2.8.E17
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q11079
    Defining formula
    A s ⁢ ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    xml-id
    C2.S8.XMD17.m1bdec
    0 references
    Q11080
    Defining formula
    B s ⁢ ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    xml-id
    C2.S8.XMD18.m1bdec
    0 references
    Q11071
    Defining formula
    ψ ⁢ ( ξ ) 𝜓 𝜉 {\displaystyle{\displaystyle\psi(\xi)}}
    xml-id
    C2.S8.XMD7.m1fdec
    0 references
     
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