DLMF:24.11.E6 (Q7521): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11169 / rank
 
Normal rank
Property / Symbols used: Q11169 / qualifier
 
Defining formula:

⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}

\floor{\NVar{x}}
Property / Symbols used: Q11169 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r17.m4aadec

Revision as of 01:42, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.11.E6
No description defined

    Statements

    Defining formula
    ( - 1 ) ⌊ ( n + 1 ) / 2 ⌋ ⁢ π n + 1 4 ⁢ ( n ! ) ⁢ E n ⁡ ( x ) → { sin ⁡ ( π ⁢ x ) , n ⁢  even , cos ⁡ ( π ⁢ x ) , n ⁢  odd , → superscript 1 𝑛 1 2 superscript 𝜋 𝑛 1 4 𝑛 Euler-polynomial-E 𝑛 𝑥 cases 𝜋 𝑥 𝑛  even 𝜋 𝑥 𝑛  odd {\displaystyle{\displaystyle(-1)^{\left\lfloor(n+1)/2\right\rfloor}\frac{\pi^{% n+1}}{4(n!)}E_{n}\left(x\right)\to\begin{cases}\sin\left(\pi x\right),&n\text{% even},\\ \cos\left(\pi x\right),&n\text{ odd},\end{cases}}}
    0 references
    DLMF id
    DLMF:24.11.E6
    0 references
    Symbols used
    Q12114
    Defining formula
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5acdec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4aadec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7521&oldid=33807"