DLMF:5.11.E2 (Q2118): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11273 / rank
 
Normal rank
Property / Symbols used: Q11273 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11273 / qualifier
 
xml-id: C5.S1.XMD7.m1adec

Latest revision as of 19:40, 1 January 2020

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DLMF:5.11.E2
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    Statements

    Defining formula
    ψ ⁡ ( z ) ∼ ln ⁡ z - 1 2 ⁢ z - ∑ k = 1 ∞ B 2 ⁢ k 2 ⁢ k ⁢ z 2 ⁢ k . asymptotic-expansion digamma 𝑧 𝑧 1 2 𝑧 superscript subscript 𝑘 1 Bernoulli-number-B 2 𝑘 2 𝑘 superscript 𝑧 2 𝑘 {\displaystyle{\displaystyle\psi\left(z\right)\sim\ln z-\frac{1}{2z}-\sum_{k=1% }^{\infty}\frac{B_{2k}}{2kz^{2k}}.}}
    0 references
    DLMF id
    DLMF:5.11.E2
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aadec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1adec
    0 references
    Q11273
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1adec
    0 references
     
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