DLMF:13.2.E23 (Q4313): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
test:

∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2aadec

Revision as of 14:38, 2 January 2020

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DLMF:13.2.E23
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    Statements

    test
    𝐌 ⁡ ( a , b , z ) ∼ e z ⁢ z a - b / Γ ⁡ ( a ) , asymptotically-equals Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 superscript 𝑒 𝑧 superscript 𝑧 𝑎 𝑏 Euler-Gamma 𝑎 {\displaystyle{\displaystyle{\mathbf{M}}\left(a,b,z\right)\sim\ifrac{e^{z}z^{a% -b}}{\Gamma\left(a\right)},}}
    0 references
    DLMF id
    DLMF:13.2.E23
    0 references
    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
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aldec
    0 references
    Olver’s confluent hypergeometric function
    test
    𝐌 ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-bold-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle{\mathbf{M}}\left(\NVar{a},\NVar{b},\NVar{z}\right% )}}
    xml-id
    C13.S2.E3.m2addec
    0 references
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
    0 references
     
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