DLMF:13.20.E5 (Q4594): Difference between revisions

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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.m2acdec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
Defining formula:

W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E3.m2aadec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: DLMF:13.20.E3 / rank
 
Normal rank
Property / Symbols used: DLMF:13.20.E3 / qualifier
 
Defining formula:

X 𝑋 {\displaystyle{\displaystyle X}}

X
Property / Symbols used: DLMF:13.20.E3 / qualifier
 
xml-id: C13.S20.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: DLMF:13.20.E3 / rank
 
Normal rank
Property / Symbols used: DLMF:13.20.E3 / qualifier
 
Defining formula:

X 𝑋 {\displaystyle{\displaystyle X}}

X
Property / Symbols used: DLMF:13.20.E3 / qualifier
 
xml-id: C13.S20.XMD1.m1bdec

Latest revision as of 16:15, 2 January 2020

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English
DLMF:13.20.E5
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( x ) = x X ⁢ ( 2 ⁢ μ 2 - κ ⁢ x + μ ⁢ X ( μ - κ ) ⁢ x ) μ ⁢ ( X + x - 2 ⁢ κ 2 ) κ ⁢ e - 1 2 ⁢ X - κ ⁢ ( 1 + O ⁡ ( 1 μ ) ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑥 𝑥 𝑋 superscript 2 superscript 𝜇 2 𝜅 𝑥 𝜇 𝑋 𝜇 𝜅 𝑥 𝜇 superscript 𝑋 𝑥 2 𝜅 2 𝜅 superscript 𝑒 1 2 𝑋 𝜅 1 Big-O 1 𝜇 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(x\right)=\sqrt{\frac{x}{X}}\*% \left(\frac{2\mu^{2}-\kappa x+\mu X}{(\mu-\kappa)x}\right)^{\mu}\*\left(\frac{% X+x-2\kappa}{2}\right)^{\kappa}\*e^{-\frac{1}{2}X-\kappa}\*\left(1+O\left(% \frac{1}{\mu}\right)\right),}}
    0 references
    DLMF id
    DLMF:13.20.E5
    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.m2acdec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q11566
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C13.S1.XMD4.m1cdec
    0 references
    DLMF:13.20.E3
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S20.XMD1.m1bdec
    0 references
    DLMF:13.20.E3
    Defining formula
    X 𝑋 {\displaystyle{\displaystyle X}}
    xml-id
    C13.S20.XMD1.m1bdec
    0 references
     
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