DLMF:5.7.E8 (Q2084)

From DRMF
Revision as of 19:34, 1 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:5.7.E8
No description defined

    Statements

    Defining formula
    ℑ ⁡ ψ ⁡ ( 1 + i ⁢ y ) = ∑ k = 1 ∞ y k 2 + y 2 . digamma 1 imaginary-unit 𝑦 superscript subscript 𝑘 1 𝑦 superscript 𝑘 2 superscript 𝑦 2 {\displaystyle{\displaystyle\Im\psi\left(1+\mathrm{i}y\right)=\sum_{k=1}^{% \infty}\frac{y}{k^{2}+y^{2}}.}}
    0 references
    DLMF id
    DLMF:5.7.E8
    0 references
    Symbols used
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2addec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1gdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2084&oldid=28663"