DLMF:27.7.E4 (Q8044): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q12237 / rank
 
Normal rank
Property / Symbols used: Q12237 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12237 / qualifier
 
xml-id: C27.S1.XMD6.m1cdec

Latest revision as of 14:20, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:27.7.E4
No description defined

    Statements

    Defining formula
    ∑ n = 1 ∞ ϕ ⁡ ( n ) ⁢ x n 1 - x n = x ( 1 - x ) 2 , superscript subscript 𝑛 1 Euler-totient-phi 𝑛 superscript 𝑥 𝑛 1 superscript 𝑥 𝑛 𝑥 superscript 1 𝑥 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\phi\left(n\right)\frac{x^{n}}{% 1-x^{n}}=\frac{x}{(1-x)^{2}},}}
    0 references
    DLMF id
    DLMF:27.7.E4
    0 references
    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
    0 references
    Symbols used
    Euler’s totient
    Defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2adec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
    0 references
    Q12237
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8044&oldid=46072"