DLMF:13.20.E19 (Q4608): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11584 / rank
 
Normal rank
Property / Symbols used: Q11584 / qualifier
 
Defining formula:

env ⁢ U ⁡ ( c , x ) envelope-Parabolic-U 𝑐 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}% \right)}}

\envparaU@{\NVar{c}}{\NVar{x}}
Property / Symbols used: Q11584 / qualifier
 
xml-id: C14.S15.SS5.p1.m7aadec

Revision as of 16:16, 2 January 2020

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DLMF:13.20.E19
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    Statements

    Defining formula
    M κ , μ ⁡ ( x ) = ( 8 ⁢ μ ) 1 4 ⁢ ( 2 ⁢ μ e ) 2 ⁢ μ ⁢ ( e κ + μ ) 1 2 ⁢ ( κ + μ ) ⁢ Φ ⁢ ( κ , μ , x ) ⁢ ( U ⁡ ( μ - κ , - ζ ⁢ 2 ⁢ μ ) + env ⁢ U ⁡ ( μ - κ , - ζ ⁢ 2 ⁢ μ ) ⁢ O ⁡ ( μ - 2 3 ) ) , Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑥 superscript 8 𝜇 1 4 superscript 2 𝜇 𝑒 2 𝜇 superscript 𝑒 𝜅 𝜇 1 2 𝜅 𝜇 Φ 𝜅 𝜇 𝑥 parabolic-U 𝜇 𝜅 𝜁 2 𝜇 envelope-Parabolic-U 𝜇 𝜅 𝜁 2 𝜇 Big-O superscript 𝜇 2 3 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(x\right)=\left(8\mu\right)^{% \frac{1}{4}}\*\left(\frac{2\mu}{e}\right)^{2\mu}\*\left(\frac{e}{\kappa+\mu}% \right)^{\frac{1}{2}(\kappa+\mu)}\*\Phi(\kappa,\mu,x)\*\left(U\left(\mu-\kappa% ,-\zeta\sqrt{2\mu}\right)+\mathrm{env}\mskip-1.0mu U\left(\mu-\kappa,-\zeta% \sqrt{2\mu}\right)O\left(\mu^{-\frac{2}{3}}\right)\right),}}
    0 references
    DLMF id
    DLMF:13.20.E19
    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.m2aidec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2addec
    0 references
    Q11584
    Defining formula
    env ⁢ U ⁡ ( c , x ) envelope-Parabolic-U 𝑐 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu U\left(\NVar{c},\NVar{x}% \right)}}
    xml-id
    C14.S15.SS5.p1.m7aadec
    0 references
     
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