Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:17.3.E6 - MaRDI portal

DLMF:17.3.E6 (Q6043)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:17.3.E6
No description defined

    Statements

    DLMF defining formula
    Cos q ⁡ ( x ) = 1 2 ⁢ ( E q ⁡ ( i ⁢ x ) + E q ⁡ ( - i ⁢ x ) ) = ∑ n = 0 ∞ ( 1 - q ) 2 ⁢ n ⁢ q n ⁢ ( 2 ⁢ n - 1 ) ⁢ ( - 1 ) n ⁢ x 2 ⁢ n ( q ; q ) 2 ⁢ n . q-Cos 𝑞 𝑥 1 2 q-Exp 𝑞 𝑖 𝑥 q-Exp 𝑞 𝑖 𝑥 superscript subscript 𝑛 0 superscript 1 𝑞 2 𝑛 superscript 𝑞 𝑛 2 𝑛 1 superscript 1 𝑛 superscript 𝑥 2 𝑛 q-Pochhammer-symbol 𝑞 𝑞 2 𝑛 {\displaystyle{\displaystyle\mathrm{Cos}_{q}\left(x\right)=\frac{1}{2}(E_{q}% \left(ix\right)+E_{q}\left(-ix\right))=\sum_{n=0}^{\infty}\frac{(1-q)^{2n}q^{n% (2n-1)}(-1)^{n}x^{2n}}{\left(q;q\right)_{2n}}.}}
    0 references
    Symbols used
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    $$q$$ -exponential function
    DLMF defining formula
    E q ⁡ ( x ) q-Exp 𝑞 𝑥 {\displaystyle{\displaystyle E_{\NVar{q}}\left(\NVar{x}\right)}}
    xml-id
    C17.S3.E2.m2abdec
    0 references
    Q11269
    DLMF defining formula
    ( a ; q ) n q-Pochhammer-symbol 𝑎 𝑞 𝑛 {\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
    xml-id
    C17.S2.SS1.p1.m2aedec
    0 references
    complex base
    DLMF defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C17.S1.XMD10.m1edec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C17.S1.XMD4.m1edec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C17.S1.XMD8.m1edec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q6043&oldid=24174412"
    Powered by MediaWiki