DLMF:26.8.E9 (Q7834): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: Q12173 / rank
 
Normal rank
Property / Symbols used: Q12173 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12173 / qualifier
 
xml-id: C26.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12174 / rank
 
Normal rank
Property / Symbols used: Q12174 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12174 / qualifier
 
xml-id: C26.S1.XMD4.m1hdec
Property / Symbols used
 
Property / Symbols used: Q12172 / rank
 
Normal rank
Property / Symbols used: Q12172 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12172 / qualifier
 
xml-id: C26.S1.XMD6.m1idec

Latest revision as of 13:52, 2 January 2020

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DLMF:26.8.E9
No description defined

    Statements

    n , k = 0 s ( n , k ) x n n ! y k = ( 1 + x ) y , superscript subscript 𝑛 𝑘 0 Stirling-number-first-kind-S 𝑛 𝑘 superscript 𝑥 𝑛 𝑛 superscript 𝑦 𝑘 superscript 1 𝑥 𝑦 {\displaystyle{\displaystyle\sum_{n,k=0}^{\infty}s\left(n,k\right)\frac{x^{n}}% {n!}y^{k}=(1+x)^{y},}}
    0 references
    DLMF:26.8.E9
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    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    s ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    C26.S8.SS1.p1.m5afdec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C26.S1.XMD1.m1bdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C26.S1.XMD4.m1hdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C26.S1.XMD6.m1idec
    0 references