DLMF:11.10.E18 (Q4036): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Lommel function / rank
 
Normal rank
Property / Symbols used: Lommel function / qualifier
 
test:

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.m2aadec
Property / Symbols used
 
Property / Symbols used: Weber function / rank
 
Normal rank
Property / Symbols used: Weber function / qualifier
 
test:

𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\WeberE{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Weber function / qualifier
 
xml-id: C11.S10.E2.m2ajdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2amdec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
test:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11491 / rank
 
Normal rank
Property / Symbols used: Q11491 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11491 / qualifier
 
xml-id: C11.S1.XMD2.m1qdec
Property / Symbols used
 
Property / Symbols used: Q11492 / rank
 
Normal rank
Property / Symbols used: Q11492 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11492 / qualifier
 
xml-id: C11.S1.XMD3.m1udec

Latest revision as of 13:56, 2 January 2020

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DLMF:11.10.E18
No description defined

    Statements

    test
    𝐄 ν ⁡ ( z ) = - 1 π ⁢ ( 1 + cos ⁡ ( π ⁢ ν ) ) ⁢ s 0 , ν ⁡ ( z ) - ν π ⁢ ( 1 - cos ⁡ ( π ⁢ ν ) ) ⁢ s - 1 , ν ⁡ ( z ) . Weber-E 𝜈 𝑧 1 𝜋 1 𝜋 𝜈 Lommel-s 0 𝜈 𝑧 𝜈 𝜋 1 𝜋 𝜈 Lommel-s 1 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\nu}\left(z\right)=-\frac{1}{\pi}(1+% \cos\left(\pi\nu\right))s_{{0},{\nu}}\left(z\right)\\ -\frac{\nu}{\pi}(1-\cos\left(\pi\nu\right))s_{{-1},{\nu}}\left(z\right).}}
    0 references
    DLMF id
    DLMF:11.10.E18
    0 references
    Symbols used
    Lommel function
    test
    s μ , ν ⁡ ( z ) Lommel-s 𝜇 𝜈 𝑧 {\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right% )}}
    xml-id
    C11.S9.E3.m2aadec
    0 references
    Weber function
    test
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2ahdec
    0 references
    Q11491
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1qdec
    0 references
    Q11492
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1udec
    0 references
     
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