DLMF:10.5.E1 (Q3024): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: Bessel function of the first kind / qualifier
 
Defining formula:

J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselJ{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Bessel function of the first kind / qualifier
 
xml-id: C10.S2.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10865 / rank
 
Normal rank
Property / Symbols used: Q10865 / qualifier
 
Defining formula:

𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}

\Wronskian
Property / Symbols used: Q10865 / qualifier
 
xml-id: C1.S13.Px2.p1.m3adec
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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11426 / rank
 
Normal rank
Property / Symbols used: Q11426 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11426 / qualifier
 
xml-id: C10.S1.XMD6.m1dec
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.m1dec

Latest revision as of 15:06, 2 January 2020

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DLMF:10.5.E1
No description defined

    Statements

    Defining formula
    𝒲 ⁡ { J ν ⁡ ( z ) , J - ν ⁡ ( z ) } = J ν + 1 ⁡ ( z ) ⁢ J - ν ⁡ ( z ) + J ν ⁡ ( z ) ⁢ J - ν - 1 ⁡ ( z ) = - 2 ⁢ sin ⁡ ( ν ⁢ π ) / ( π ⁢ z ) , Wronskian Bessel-J 𝜈 𝑧 Bessel-J 𝜈 𝑧 Bessel-J 𝜈 1 𝑧 Bessel-J 𝜈 𝑧 Bessel-J 𝜈 𝑧 Bessel-J 𝜈 1 𝑧 2 𝜈 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{J_{\nu}\left(z\right),J_{-\nu}% \left(z\right)\right\}=J_{\nu+1}\left(z\right)J_{-\nu}\left(z\right)+J_{\nu}% \left(z\right)J_{-\nu-1}\left(z\right)=-2\sin\left(\nu\pi\right)/(\pi z),}}
    0 references
    DLMF id
    DLMF:10.5.E1
    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.m2adec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    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
    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.m1dec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references
     
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