DLMF:5.15.E6 (Q2175): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: Q11274 / rank
 
Normal rank
Property / Symbols used: Q11274 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11274 / qualifier
 
xml-id: C5.S1.XMD3.m1ddec

Revision as of 00:07, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:5.15.E6
No description defined

    Statements

    test
    ψ ( n ) ⁡ ( 1 - z ) + ( - 1 ) n - 1 ⁢ ψ ( n ) ⁡ ( z ) = ( - 1 ) n ⁢ π ⁢ d n d z n ⁡ cot ⁡ ( π ⁢ z ) , digamma 𝑛 1 𝑧 superscript 1 𝑛 1 digamma 𝑛 𝑧 superscript 1 𝑛 𝜋 derivative 𝑧 𝑛 𝜋 𝑧 {\displaystyle{\displaystyle{\psi^{(n)}}\left(1-z\right)+(-1)^{n-1}{\psi^{(n)}% }\left(z\right)=(-1)^{n}\pi\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\cot\left% (\pi z\right),}}
    0 references
    DLMF id
    DLMF:5.15.E6
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cotangent function
    test
    cot ⁡ z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    xml-id
    C4.S14.E7.m2adec
    0 references
    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2adec
    0 references
    psi (or digamma) function
    test
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2acdec
    0 references
    Q11274
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C5.S1.XMD3.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2175&oldid=10596"