DLMF:5.4.E15 (Q2053): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2acdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11274 / rank
 
Normal rank
Property / Symbols used: Q11274 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11274 / qualifier
 
xml-id: C5.S1.XMD3.m1cdec

Latest revision as of 19:29, 1 January 2020

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DLMF:5.4.E15
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    Statements

    ψ ( n + 1 2 ) = - γ - 2 ln 2 + 2 ( 1 + 1 3 + + 1 2 n - 1 ) , digamma 𝑛 1 2 2 2 2 1 1 3 1 2 𝑛 1 {\displaystyle{\displaystyle\psi\left(n+\tfrac{1}{2}\right)=-\gamma-2\ln 2+2% \left(1+\tfrac{1}{3}+\dots+\tfrac{1}{2n-1}\right),}}
    0 references
    DLMF:5.4.E15
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    n = 1 , 2 , 𝑛 1 2 {\displaystyle{\displaystyle n=1,2,\dots}}
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    γ {\displaystyle{\displaystyle\gamma}}
    C5.S2.E3.m2addec
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    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2acdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C5.S1.XMD3.m1cdec
    0 references