DLMF:5.4.E18 (Q2056): 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: hyperbolic cotangent function / rank
 
Normal rank
Property / Symbols used: hyperbolic cotangent function / qualifier
 
Defining formula:

coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}

\coth@@{\NVar{z}}
Property / Symbols used: hyperbolic cotangent function / qualifier
 
xml-id: C4.S28.E7.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aedec
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.m1edec

Latest revision as of 19:30, 1 January 2020

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DLMF:5.4.E18
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    Statements

    ψ ( 1 + i y ) = - 1 2 y + π 2 coth ( π y ) . digamma 1 𝑖 𝑦 1 2 𝑦 𝜋 2 hyperbolic-cotangent 𝜋 𝑦 {\displaystyle{\displaystyle\Im\psi\left(1+iy\right)=-\frac{1}{2y}+\frac{\pi}{% 2}\coth\left(\pi y\right).}}
    0 references
    DLMF:5.4.E18
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aidec
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    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2afdec
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    coth z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    C4.S28.E7.m2aadec
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    absent {\displaystyle{\displaystyle\Im}}
    C1.S9.E2.m2abdec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2aedec
    0 references
    y 𝑦 {\displaystyle{\displaystyle y}}
    C5.S1.XMD6.m1edec
    0 references