DLMF:10.2.E3 (Q3007): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11427 / rank
 
Normal rank
Property / Symbols used: Q11427 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

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

Latest revision as of 15:05, 2 January 2020

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DLMF:10.2.E3
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    Statements

    Defining formula
    Y ν ⁡ ( z ) = J ν ⁡ ( z ) ⁢ cos ⁡ ( ν ⁢ π ) - J - ν ⁡ ( z ) sin ⁡ ( ν ⁢ π ) . Bessel-Y-Weber 𝜈 𝑧 Bessel-J 𝜈 𝑧 𝜈 𝜋 Bessel-J 𝜈 𝑧 𝜈 𝜋 {\displaystyle{\displaystyle Y_{\nu}\left(z\right)=\frac{J_{\nu}\left(z\right)% \cos\left(\nu\pi\right)-J_{-\nu}\left(z\right)}{\sin\left(\nu\pi\right)}.}}
    0 references
    DLMF id
    DLMF:10.2.E3
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1bdec
    0 references
     
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