DLMF:26.8.E31 (Q7859): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11097 / rank
 
Normal rank
Property / Symbols used: Q11097 / qualifier
 
Defining formula:

Δ forward-difference {\displaystyle{\displaystyle\Delta}}

\fDiff
Property / Symbols used: Q11097 / qualifier
 
xml-id: C3.S6.SS1.p1.m2adec

Revision as of 13:55, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:26.8.E31
No description defined

    Statements

    1 k ! d k d x k f ( x ) = n = k s ( n , k ) n ! Δ n f ( x ) , 1 𝑘 derivative 𝑥 𝑘 𝑓 𝑥 superscript subscript 𝑛 𝑘 Stirling-number-first-kind-S 𝑛 𝑘 𝑛 superscript forward-difference 𝑛 𝑓 𝑥 {\displaystyle{\displaystyle\frac{1}{k!}\,\frac{{\mathrm{d}}^{k}}{{\mathrm{d}x% }^{k}}f(x)=\sum_{n=k}^{\infty}\frac{s\left(n,k\right)}{n!}\,\Delta^{n}f(x),}}
    0 references
    DLMF:26.8.E31
    0 references
    s ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    C26.S8.SS1.p1.m5ardec
    0 references
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    C1.S4.E4.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aidec
    0 references
    Δ forward-difference {\displaystyle{\displaystyle\Delta}}
    C3.S6.SS1.p1.m2adec
    0 references