DLMF:33.12.E2 (Q9596): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12670 / rank
 
Normal rank
Property / Symbols used: Q12670 / qualifier
 
Defining formula:

G ℓ ⁡ ( η , ρ ) irregular-Coulomb-G ℓ 𝜂 𝜌 {\displaystyle{\displaystyle G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}% \right)}}

\irregCoulombG{\NVar{\ell}}@{\NVar{\eta}}{\NVar{\rho}}
Property / Symbols used: Q12670 / qualifier
 
xml-id: C33.S2.E11.m1adec

Revision as of 14:29, 2 January 2020

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DLMF:33.12.E2
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    Statements

    Defining formula
    F 0 ⁡ ( η , ρ ) G 0 ⁡ ( η , ρ ) ∼ π 1 / 2 ⁢ ( 2 ⁢ η ) 1 / 6 ⁢ { Ai ⁡ ( x ) Bi ⁡ ( x ) ⁢ ( 1 + B 1 μ + B 2 μ 2 + ⋯ ) + Ai ′ ⁡ ( x ) Bi ′ ⁡ ( x ) ⁢ ( A 1 μ + A 2 μ 2 + ⋯ ) } , asymptotic-expansion FRACOP regular-Coulomb-F 0 𝜂 𝜌 irregular-Coulomb-G 0 𝜂 𝜌 superscript 𝜋 1 2 superscript 2 𝜂 1 6 FRACOP Airy-Ai 𝑥 Airy-Bi 𝑥 1 subscript 𝐵 1 𝜇 subscript 𝐵 2 superscript 𝜇 2 ⋯ FRACOP diffop Airy-Ai 1 𝑥 diffop Airy-Bi 1 𝑥 subscript 𝐴 1 𝜇 subscript 𝐴 2 superscript 𝜇 2 ⋯ {\displaystyle{\displaystyle{F_{0}\left(\eta,\rho\right)\atop G_{0}\left(\eta,% \rho\right)}\sim\pi^{1/2}(2\eta)^{1/6}\left\{{\mathrm{Ai}\left(x\right)\atop% \mathrm{Bi}\left(x\right)}\left(1+\frac{B_{1}}{\mu}+\frac{B_{2}}{\mu^{2}}+% \cdots\right)+{\mathrm{Ai}'\left(x\right)\atop\mathrm{Bi}'\left(x\right)}\left% (\frac{A_{1}}{\mu}+\frac{A_{2}}{\mu^{2}}+\cdots\right)\right\},}}
    0 references
    DLMF id
    DLMF:33.12.E2
    0 references
    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1adec
    0 references
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    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
    Q12670
    Defining formula
    G ℓ ⁡ ( η , ρ ) irregular-Coulomb-G ℓ 𝜂 𝜌 {\displaystyle{\displaystyle G_{\NVar{\ell}}\left(\NVar{\eta},\NVar{\rho}% \right)}}
    xml-id
    C33.S2.E11.m1adec
    0 references
     
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