DLMF:10.21.E23 (Q3307): Difference between revisions

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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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11430 / rank
 
Normal rank
Property / Symbols used: Q11430 / qualifier
 
Defining formula:

𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}

\BesselC{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: Q11430 / qualifier
 
xml-id: C10.S2.Px5.p1.m3addec
Property / Symbols used
 
Property / Symbols used: Airy modulus function / rank
 
Normal rank
Property / Symbols used: Airy modulus function / qualifier
 
Defining formula:

M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}

\AirymodM@{\NVar{z}}
Property / Symbols used: Airy modulus function / qualifier
 
xml-id: C9.S8.E3.m2adec
Property / Symbols used
 
Property / Symbols used: Q11428 / rank
 
Normal rank
Property / Symbols used: Q11428 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11428 / qualifier
 
xml-id: C10.S1.XMD3.m1cdec
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.m1udec
Property / Symbols used
 
Property / Symbols used: Q11460 / rank
 
Normal rank
Property / Symbols used: Q11460 / qualifier
 
Defining formula:

ρ ν ⁢ ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}

\rho_{\nu}(t)
Property / Symbols used: Q11460 / qualifier
 
xml-id: C10.S21.XMD1.m1gdec
Property / Symbols used
 
Property / Symbols used: coefficients (locally) / rank
 
Normal rank
Property / Symbols used: coefficients (locally) / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: coefficients (locally) / qualifier
 
xml-id: C10.S21.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: Q11463 / rank
 
Normal rank
Property / Symbols used: Q11463 / qualifier
 
Defining formula:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q11463 / qualifier
 
xml-id: C10.S21.XMD5.m1dec

Latest revision as of 15:43, 2 January 2020

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English
DLMF:10.21.E23
No description defined

    Statements

    Defining formula
    𝒞 ν ′ ⁡ ( ρ ν ⁢ ( t ) ) ∼ ( 2 / ν ) 2 3 π ⁢ M ⁡ ( - 2 1 3 ⁢ α ) ⁢ ∑ k = 0 ∞ β k ν 2 ⁢ k / 3 , asymptotic-expansion diffop cylinder-function 𝜈 1 subscript 𝜌 𝜈 𝑡 superscript 2 𝜈 2 3 𝜋 modulus-Airy-M superscript 2 1 3 𝛼 superscript subscript 𝑘 0 subscript 𝛽 𝑘 superscript 𝜈 2 𝑘 3 {\displaystyle{\displaystyle\mathscr{C}_{\nu}'\left(\rho_{\nu}(t)\right)\sim% \frac{(2/\nu)^{\frac{2}{3}}}{\pi M\left(-2^{\frac{1}{3}}\alpha\right)}\sum_{k=% 0}^{\infty}\frac{\beta_{k}}{\nu^{2k/3}},}}
    0 references
    DLMF id
    DLMF:10.21.E23
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3addec
    0 references
    Airy modulus function
    Defining formula
    M ⁡ ( z ) modulus-Airy-M 𝑧 {\displaystyle{\displaystyle M\left(\NVar{z}\right)}}
    xml-id
    C9.S8.E3.m2adec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1cdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1udec
    0 references
    Q11460
    Defining formula
    ρ ν ⁢ ( t ) subscript 𝜌 𝜈 𝑡 {\displaystyle{\displaystyle\rho_{\nu}(t)}}
    xml-id
    C10.S21.XMD1.m1gdec
    0 references
    coefficients (locally)
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C10.S21.XMD4.m1adec
    0 references
    Q11463
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C10.S21.XMD5.m1dec
    0 references
     
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