DLMF:5.7.E8 (Q2084): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11278 / rank
 
Normal rank
Property / Symbols used: Q11278 / qualifier
 
Defining formula:

y 𝑦 {\displaystyle{\displaystyle y}}

y
Property / Symbols used: Q11278 / qualifier
 
xml-id: C5.S1.XMD6.m1dec

Latest revision as of 19:34, 1 January 2020

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DLMF:5.7.E8
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    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
    Q11278
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C5.S1.XMD6.m1dec
    0 references
     
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