DLMF:13.14.E20 (Q4509): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1sdec

Revision as of 16:06, 2 January 2020

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DLMF:13.14.E20
No description defined

    Statements

    Defining formula
    M κ , μ ⁡ ( z ) ∼ Γ ⁡ ( 1 + 2 ⁢ μ ) ⁢ e 1 2 ⁢ z ⁢ z - κ / Γ ⁡ ( 1 2 + μ - κ ) , asymptotically-equals Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Euler-Gamma 1 2 𝜇 superscript 𝑒 1 2 𝑧 superscript 𝑧 𝜅 Euler-Gamma 1 2 𝜇 𝜅 {\displaystyle{\displaystyle M_{\kappa,\mu}\left(z\right)\sim\ifrac{\Gamma% \left(1+2\mu\right)e^{\frac{1}{2}z}z^{-\kappa}}{\Gamma\left(\tfrac{1}{2}+\mu-% \kappa\right)},}}
    0 references
    DLMF id
    DLMF:13.14.E20
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    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle\left|\operatorname{ph}z\right|\leq\frac{1}{2}\pi-% \delta}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    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.m2ahdec
    0 references
    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2adec
    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aldec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1sdec
    0 references
     
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