DLMF:4.19.E9 (Q1688)

From DRMF
Revision as of 18:22, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:4.19.E9
No description defined

    Statements

    Defining formula
    ln ⁡ ( tan ⁡ z z ) = ∑ n = 1 ∞ ( - 1 ) n - 1 ⁢ 2 2 ⁢ n ⁢ ( 2 2 ⁢ n - 1 - 1 ) ⁢ B 2 ⁢ n n ⁢ ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n , 𝑧 𝑧 superscript subscript 𝑛 1 superscript 1 𝑛 1 superscript 2 2 𝑛 superscript 2 2 𝑛 1 1 Bernoulli-number-B 2 𝑛 𝑛 2 𝑛 superscript 𝑧 2 𝑛 {\displaystyle{\displaystyle\ln\left(\frac{\tan z}{z}\right)=\sum_{n=1}^{% \infty}\frac{(-1)^{n-1}2^{2n}(2^{2n-1}-1)B_{2n}}{n(2n)!}z^{2n},}}
    0 references
    DLMF id
    DLMF:4.19.E9
    0 references
    constraint
    | z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5ahdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    tangent function
    Defining formula
    tan ⁡ z 𝑧 {\displaystyle{\displaystyle\tan\NVar{z}}}
    xml-id
    C4.S14.E4.m2aadec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1fdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1688&oldid=27157"