DLMF:11.9.E2 (Q4009): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Bessel function of the second kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the second kind / qualifier
 
Defining formula:

Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselY{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the second kind / qualifier
 
xml-id: C10.S2.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Lommel function / rank
 
Normal rank
Property / Symbols used: Lommel function / qualifier
 
Defining formula:

s μ , ν ( z ) Lommel-s 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}

\Lommels{\NVar{\mu}}{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Lommel function / qualifier
 
xml-id: C11.S9.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11502 / rank
 
Normal rank
Property / Symbols used: Q11502 / qualifier
 
Defining formula:

A 𝐴 {\displaystyle{\displaystyle A}}

A
Property / Symbols used: Q11502 / qualifier
 
xml-id: C11.S9.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q11503 / rank
 
Normal rank
Property / Symbols used: Q11503 / qualifier
 
Defining formula:

B 𝐵 {\displaystyle{\displaystyle B}}

B
Property / Symbols used: Q11503 / qualifier
 
xml-id: C11.S9.XMD2.m1dec

Latest revision as of 14:52, 2 January 2020

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DLMF:11.9.E2
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    Statements

    w = s μ , ν ( z ) + A J ν ( z ) + B Y ν ( z ) , 𝑤 Lommel-s 𝜇 𝜈 𝑧 𝐴 Bessel-J 𝜈 𝑧 𝐵 Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle w=s_{{\mu},{\nu}}\left(z\right)+AJ_{\nu}\left(z% \right)+BY_{\nu}\left(z\right),}}
    0 references
    DLMF:11.9.E2
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2adec
    0 references
    Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E3.m2adec
    0 references
    s μ , ν ( z ) Lommel-s 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}
    C11.S9.E3.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C11.S1.XMD2.m1adec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C11.S1.XMD3.m1adec
    0 references
    A 𝐴 {\displaystyle{\displaystyle A}}
    C11.S9.XMD1.m1dec
    0 references
    B 𝐵 {\displaystyle{\displaystyle B}}
    C11.S9.XMD2.m1dec
    0 references