DLMF:13.29.E8 (Q4675): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11559 / rank
 
Normal rank
Property / Symbols used: Q11559 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11559 / qualifier
 
xml-id: C13.S1.XMD2.m1edec

Revision as of 01:09, 2 January 2020

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DLMF:13.29.E8
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    Statements

    Defining formula
    w ⁢ ( n ) ∼ π ⁢ e 1 2 ⁢ z ⁢ z 1 4 ⁢ ( 4 ⁢ a - 2 ⁢ b + 1 ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( a + 1 - b ) ⁢ n 1 4 ⁢ ( 4 ⁢ a - 2 ⁢ b - 3 ) ⁢ e - 2 ⁢ n ⁢ z , asymptotically-equals 𝑤 𝑛 𝜋 superscript 𝑒 1 2 𝑧 superscript 𝑧 1 4 4 𝑎 2 𝑏 1 Euler-Gamma 𝑎 Euler-Gamma 𝑎 1 𝑏 superscript 𝑛 1 4 4 𝑎 2 𝑏 3 superscript 𝑒 2 𝑛 𝑧 {\displaystyle{\displaystyle w(n)\sim\frac{\sqrt{\pi}e^{\frac{1}{2}z}z^{\frac{% 1}{4}(4a-2b+1)}}{\Gamma\left(a\right)\Gamma\left(a+1-b\right)}n^{\frac{1}{4}(4% a-2b-3)}e^{-2\sqrt{nz}},}}
    0 references
    DLMF id
    DLMF:13.29.E8
    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.m2adec
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q11559
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C13.S1.XMD2.m1edec
    0 references
     
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