DLMF:13.20.E17 (Q4606): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11566 / rank
 
Normal rank
Property / Symbols used: Q11566 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11566 / qualifier
 
xml-id: C13.S1.XMD4.m1ndec

Revision as of 16:16, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.20.E17
No description defined

    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-bar 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 \overline{U}\left(\mu-% \kappa,\zeta\sqrt{2\mu}\right)O\left(\mu^{-\frac{2}{3}}\right)\right),}}
    0 references
    DLMF id
    DLMF:13.20.E17
    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.m2agdec
    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.m2acdec
    0 references
    Q11585
    Defining formula
    env ⁢ U ¯ ⁡ ( c , x ) envelope-Parabolic-U-bar 𝑐 𝑥 {\displaystyle{\displaystyle\mathrm{env}\mskip-1.0mu \overline{U}\left(\NVar{c% },\NVar{x}\right)}}
    xml-id
    C14.S15.SS5.p1.m9adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    Q11320
    Defining formula
    U ⁡ ( a , z ) parabolic-U 𝑎 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C12.S2.SS1.p1.m1acdec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1ndec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4606&oldid=63168"