DLMF:5.9.E15 (Q2104)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:5.9.E15
No description defined

    Statements

    test
    ψ ⁡ ( z ) = ln ⁡ z - 1 2 ⁢ z - 2 ⁢ ∫ 0 ∞ t ⁢ d t ( t 2 + z 2 ) ⁢ ( e 2 ⁢ π ⁢ t - 1 ) . digamma 𝑧 𝑧 1 2 𝑧 2 superscript subscript 0 𝑡 𝑡 superscript 𝑡 2 superscript 𝑧 2 superscript 𝑒 2 𝜋 𝑡 1 {\displaystyle{\displaystyle\psi\left(z\right)=\ln z-\frac{1}{2z}-2\int_{0}^{% \infty}\frac{t\mathrm{d}t}{(t^{2}+z^{2})(e^{2\pi t}-1)}.}}
    0 references
    DLMF id
    DLMF:5.9.E15
    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.m2agdec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    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
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    principal branch of logarithm function
    test
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11273
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C5.S1.XMD7.m1ldec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2104&oldid=10132"