DLMF:18.12.E9 (Q5651)

From DRMF
Revision as of 15:32, 2 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:18.12.E9
No description defined

    Statements

    Defining formula
    - ln ⁡ ( 1 - 2 ⁢ x ⁢ z + z 2 ) = 2 ⁢ ∑ n = 1 ∞ T n ⁡ ( x ) n ⁢ z n , 1 2 𝑥 𝑧 superscript 𝑧 2 2 superscript subscript 𝑛 1 Chebyshev-polynomial-first-kind-T 𝑛 𝑥 𝑛 superscript 𝑧 𝑛 {\displaystyle{\displaystyle-\ln\left(1-2xz+z^{2}\right)=2\sum_{n=1}^{\infty}% \frac{T_{n}\left(x\right)}{n}z^{n},}}
    0 references
    DLMF id
    DLMF:18.12.E9
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    Q11207
    Defining formula
    T n ⁡ ( x ) Chebyshev-polynomial-first-kind-T 𝑛 𝑥 {\displaystyle{\displaystyle T_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r4.m2abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1hdec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1hdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5651&oldid=58599"