DLMF:10.4.E5 (Q3019): Difference between revisions

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

csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}

\csc@@{\NVar{z}}
Property / Symbols used: cosecant function / qualifier
 
xml-id: C4.S14.E5.m2adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
test:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q11427 / qualifier
 
xml-id: C10.S1.XMD7.m1bdec

Latest revision as of 15:06, 2 January 2020

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DLMF:10.4.E5
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    Statements

    J ν ( z ) = csc ( ν π ) ( Y - ν ( z ) - Y ν ( z ) cos ( ν π ) ) . Bessel-J 𝜈 𝑧 𝜈 𝜋 Bessel-Y-Weber 𝜈 𝑧 Bessel-Y-Weber 𝜈 𝑧 𝜈 𝜋 {\displaystyle{\displaystyle J_{\nu}\left(z\right)=\csc\left(\nu\pi\right)% \left(Y_{-\nu}\left(z\right)-Y_{\nu}\left(z\right)\cos\left(\nu\pi\right)% \right).}}
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    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2acdec
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    Y ν ( z ) Bessel-Y-Weber 𝜈 𝑧 {\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E3.m2acdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
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    csc z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    C4.S14.E5.m2adec
    0 references
    cos z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    C4.S14.E2.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C10.S1.XMD6.m1ddec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C10.S1.XMD7.m1bdec
    0 references