DLMF:10.21.E41 (Q3348): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
Defining formula:

O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11394 / rank
 
Normal rank
Property / Symbols used: Q11394 / qualifier
 
Defining formula:

a k zero-Airy-Ai 𝑘 {\displaystyle{\displaystyle a_{\NVar{k}}}}

\zAirya{\NVar{k}}
Property / Symbols used: Q11394 / qualifier
 
xml-id: C9.S9.SS1.p1.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11456 / rank
 
Normal rank
Property / Symbols used: Q11456 / qualifier
 
Defining formula:

j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}

\zBesselj{\NVar{\nu}}{\NVar{m}}
Property / Symbols used: Q11456 / qualifier
 
xml-id: C10.S21.SS1.p2.m11amdec
Property / Symbols used
 
Property / Symbols used: Q11438 / rank
 
Normal rank
Property / Symbols used: Q11438 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11438 / qualifier
 
xml-id: C10.S1.XMD1.m1pdec
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.m1agdec
Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
Defining formula:

B k ⁢ ( ζ ) subscript 𝐵 𝑘 𝜁 {\displaystyle{\displaystyle B_{k}(\zeta)}}

B_{k}(\zeta)
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C10.S20.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11464 / rank
 
Normal rank
Property / Symbols used: Q11464 / qualifier
 
Defining formula:

z ⁢ ( ζ ) 𝑧 𝜁 {\displaystyle{\displaystyle z(\zeta)}}

z(\zeta)
Property / Symbols used: Q11464 / qualifier
 
xml-id: C10.S21.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

h ⁢ ( ζ ) ℎ 𝜁 {\displaystyle{\displaystyle h(\zeta)}}

h(\zeta)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C10.S21.XMD8.m1dec

Latest revision as of 15:46, 2 January 2020

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DLMF:10.21.E41
No description defined

    Statements

    Defining formula
    j ν , m = ν ⁢ z ⁢ ( ζ ) + z ⁢ ( ζ ) ⁢ ( h ⁢ ( ζ ) ) 2 ⁢ B 0 ⁢ ( ζ ) 2 ⁢ ν + O ⁡ ( 1 ν 3 ) , zero-Bessel-J 𝜈 𝑚 𝜈 𝑧 𝜁 𝑧 𝜁 superscript ℎ 𝜁 2 subscript 𝐵 0 𝜁 2 𝜈 Big-O 1 superscript 𝜈 3 {\displaystyle{\displaystyle j_{\nu,m}=\nu z(\zeta)+\frac{z(\zeta)(h(\zeta))^{% 2}B_{0}(\zeta)}{2\nu}+O\left(\frac{1}{\nu^{3}}\right),}}
    0 references
    DLMF id
    DLMF:10.21.E41
    0 references
    constraint
    ζ = ν - 2 3 ⁢ a m 𝜁 superscript 𝜈 2 3 zero-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a_{m}}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    Q11394
    Defining formula
    a k zero-Airy-Ai 𝑘 {\displaystyle{\displaystyle a_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p1.m5aadec
    0 references
    Q11456
    Defining formula
    j ν , m zero-Bessel-J 𝜈 𝑚 {\displaystyle{\displaystyle j_{\NVar{\nu},\NVar{m}}}}
    xml-id
    C10.S21.SS1.p2.m11amdec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1pdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1agdec
    0 references
    coefficients (locally)
    Defining formula
    B k ⁢ ( ζ ) subscript 𝐵 𝑘 𝜁 {\displaystyle{\displaystyle B_{k}(\zeta)}}
    xml-id
    C10.S20.XMD5.m1dec
    0 references
    Q11464
    Defining formula
    z ⁢ ( ζ ) 𝑧 𝜁 {\displaystyle{\displaystyle z(\zeta)}}
    xml-id
    C10.S21.XMD7.m1dec
    0 references
    function (locally)
    Defining formula
    h ⁢ ( ζ ) ℎ 𝜁 {\displaystyle{\displaystyle h(\zeta)}}
    xml-id
    C10.S21.XMD8.m1dec
    0 references
     
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