DLMF:10.21.E43 (Q3350): Difference between revisions

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Property / constraint
 

ζ = ν - 2 3 ⁢ a m ′ 𝜁 superscript 𝜈 2 3 zero-derivative-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a^{\prime}_{m}}}

\zeta=\nu^{-\frac{2}{3}}\zderivAirya{m}
Property / constraint: ζ = ν - 2 3 ⁢ a m ′ 𝜁 superscript 𝜈 2 3 zero-derivative-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a^{\prime}_{m}}} / rank
 
Normal rank
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.m2abdec
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.m11aodec
Property / Symbols used
 
Property / Symbols used: Q11395 / rank
 
Normal rank
Property / Symbols used: Q11395 / qualifier
 
Defining formula:

a k ′ zero-derivative-Airy-Ai 𝑘 {\displaystyle{\displaystyle a^{\prime}_{\NVar{k}}}}

\zderivAirya{\NVar{k}}
Property / Symbols used: Q11395 / qualifier
 
xml-id: C9.S9.SS1.p1.m11aadec
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.m1rdec
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.m1aidec
Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
Defining formula:

C k ⁢ ( ζ ) subscript 𝐶 𝑘 𝜁 {\displaystyle{\displaystyle C_{k}(\zeta)}}

C_{k}(\zeta)
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C10.S20.XMD6.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.m1bdec
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.m1bdec

Latest revision as of 15:47, 2 January 2020

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DLMF:10.21.E43
No description defined

    Statements

    Defining formula
    j ν , m ′ = ν ⁢ z ⁢ ( ζ ) + z ⁢ ( ζ ) ⁢ ( h ⁢ ( ζ ) ) 2 ⁢ C 0 ⁢ ( ζ ) 2 ⁢ ζ ⁢ ν + O ⁡ ( 1 ν ) , diffop zero-Bessel-J 𝜈 𝑚 1 𝜈 𝑧 𝜁 𝑧 𝜁 superscript ℎ 𝜁 2 subscript 𝐶 0 𝜁 2 𝜁 𝜈 Big-O 1 𝜈 {\displaystyle{\displaystyle j_{\nu,m}'=\nu z(\zeta)+\frac{z(\zeta)(h(\zeta))^% {2}C_{0}(\zeta)}{2\zeta\nu}+O\left(\frac{1}{\nu}\right),}}
    0 references
    DLMF id
    DLMF:10.21.E43
    0 references
    constraint
    ζ = ν - 2 3 ⁢ a m ′ 𝜁 superscript 𝜈 2 3 zero-derivative-Airy-Ai 𝑚 {\displaystyle{\displaystyle\zeta=\nu^{-\frac{2}{3}}a^{\prime}_{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.m2abdec
    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.m11aodec
    0 references
    Q11395
    Defining formula
    a k ′ zero-derivative-Airy-Ai 𝑘 {\displaystyle{\displaystyle a^{\prime}_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p1.m11aadec
    0 references
    Q11438
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C10.S1.XMD1.m1rdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1aidec
    0 references
    coefficients (locally)
    Defining formula
    C k ⁢ ( ζ ) subscript 𝐶 𝑘 𝜁 {\displaystyle{\displaystyle C_{k}(\zeta)}}
    xml-id
    C10.S20.XMD6.m1dec
    0 references
    Q11464
    Defining formula
    z ⁢ ( ζ ) 𝑧 𝜁 {\displaystyle{\displaystyle z(\zeta)}}
    xml-id
    C10.S21.XMD7.m1bdec
    0 references
    function (locally)
    Defining formula
    h ⁢ ( ζ ) ℎ 𝜁 {\displaystyle{\displaystyle h(\zeta)}}
    xml-id
    C10.S21.XMD8.m1bdec
    0 references
     
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