DLMF:13.9.E9 (Q4452)

From DRMF
Revision as of 16:00, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:13.9.E9
No description defined

    Statements

    Defining formula
    z = ± ( 2 ⁢ n + a ) ⁢ π ⁢ i + ln ⁡ ( - Γ ⁡ ( a ) Γ ⁡ ( b - a ) ⁢ ( ± 2 ⁢ n ⁢ π ⁢ i ) b - 2 ⁢ a ) + O ⁡ ( n - 1 ⁢ ln ⁡ n ) , 𝑧 plus-or-minus 2 𝑛 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑎 Euler-Gamma 𝑏 𝑎 superscript plus-or-minus 2 𝑛 𝜋 imaginary-unit 𝑏 2 𝑎 Big-O superscript 𝑛 1 𝑛 {\displaystyle{\displaystyle z=\pm(2n+a)\pi\mathrm{i}+\ln\left(-\frac{\Gamma% \left(a\right)}{\Gamma\left(b-a\right)}\left(\pm 2n\pi\mathrm{i}\right)^{b-2a}% \right)+O\left(n^{-1}\ln n\right),}}
    0 references
    DLMF id
    DLMF:13.9.E9
    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.m2aadec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.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
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4452&oldid=62117"