DLMF:2.8.E27 (Q962): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3afdec
Property / Symbols used
 
Property / Symbols used: Q11086 / rank
 
Normal rank
Property / Symbols used: Q11086 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11086 / qualifier
 
xml-id: C2.S8.XMD21.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11088 / rank
 
Normal rank
Property / Symbols used: Q11088 / qualifier
 
Defining formula:

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

A_{s}(\xi)
Property / Symbols used: Q11088 / qualifier
 
xml-id: C2.S8.XMD23.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11089 / rank
 
Normal rank
Property / Symbols used: Q11089 / qualifier
 
Defining formula:

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

B_{s}(\xi)
Property / Symbols used: Q11089 / qualifier
 
xml-id: C2.S8.XMD24.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.m1idec

Latest revision as of 17:29, 1 January 2020

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DLMF:2.8.E27
No description defined

    Statements

    B s ( ξ ) = - A s ( ξ ) + 1 ξ 1 / 2 0 ξ ( ψ ( v ) A s ( v ) - ( ν + 1 2 ) A s ( v ) ) d v v 1 / 2 , subscript 𝐵 𝑠 𝜉 superscript subscript 𝐴 𝑠 𝜉 1 superscript 𝜉 1 2 superscript subscript 0 𝜉 𝜓 𝑣 subscript 𝐴 𝑠 𝑣 𝜈 1 2 superscript subscript 𝐴 𝑠 𝑣 𝑣 superscript 𝑣 1 2 {\displaystyle{\displaystyle B_{s}(\xi)=-A_{s}^{\prime}(\xi)+\frac{1}{\xi^{1/2% }}\int_{0}^{\xi}\left(\psi(v)A_{s}(v)-\left(\nu+\tfrac{1}{2}\right)A_{s}^{% \prime}(v)\right)\frac{\mathrm{d}v}{v^{1/2}},}}
    0 references
    DLMF:2.8.E27
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1afdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3afdec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C2.S8.XMD21.m1cdec
    0 references
    A s ( ξ ) subscript 𝐴 𝑠 𝜉 {\displaystyle{\displaystyle A_{s}(\xi)}}
    C2.S8.XMD23.m1bdec
    0 references
    B s ( ξ ) subscript 𝐵 𝑠 𝜉 {\displaystyle{\displaystyle B_{s}(\xi)}}
    C2.S8.XMD24.m1bdec
    0 references
    ψ ( ξ ) 𝜓 𝜉 {\displaystyle{\displaystyle\psi(\xi)}}
    C2.S8.XMD7.m1idec
    0 references