DLMF:10.5.E3 (Q3026): 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 15:07, 2 January 2020

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DLMF:10.5.E3
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    Statements

    Defining formula
    𝒲 ⁡ { J ν ⁡ ( z ) , H ν ( 1 ) ⁡ ( z ) } = J ν + 1 ⁡ ( z ) ⁢ H ν ( 1 ) ⁡ ( z ) - J ν ⁡ ( z ) ⁢ H ν + 1 ( 1 ) ⁡ ( z ) = 2 ⁢ i / ( π ⁢ z ) , Wronskian Bessel-J 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Bessel-J 𝜈 1 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 𝑧 Bessel-J 𝜈 𝑧 Hankel-H-1-Bessel-third-kind 𝜈 1 𝑧 2 𝑖 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{J_{\nu}\left(z\right),{H^{(1)}_{% \nu}}\left(z\right)\right\}=J_{\nu+1}\left(z\right){H^{(1)}_{\nu}}\left(z% \right)-J_{\nu}\left(z\right){H^{(1)}_{\nu+1}}\left(z\right)=2i/(\pi z),}}
    0 references
    DLMF id
    DLMF:10.5.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.m2abdec
    0 references
    Bessel function of the third kind (or Hankel function)
    Defining formula
    H ν ( 1 ) ⁡ ( z ) Hankel-H-1-Bessel-third-kind 𝜈 𝑧 {\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E5.m2adec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.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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