DLMF:24.17.E1 (Q7584): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12142 / rank
 
Normal rank
Property / Symbols used: Q12142 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12142 / qualifier
 
xml-id: C24.S17.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q12143 / rank
 
Normal rank
Property / Symbols used: Q12143 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12143 / qualifier
 
xml-id: C24.S17.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12144 / rank
 
Normal rank
Property / Symbols used: Q12144 / qualifier
 
Defining formula:

f ( m ) ⁢ ( x ) superscript 𝑓 𝑚 𝑥 {\displaystyle{\displaystyle f^{(m)}(x)}}

f^{(m)}(x)
Property / Symbols used: Q12144 / qualifier
 
xml-id: C24.S17.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q12145 / rank
 
Normal rank
Property / Symbols used: Q12145 / qualifier
 
Defining formula:

R m ⁢ ( n ) subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle R_{m}(n)}}

R_{m}(n)
Property / Symbols used: Q12145 / qualifier
 
xml-id: C24.S17.XMD5.m1dec

Latest revision as of 01:52, 2 January 2020

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DLMF:24.17.E1
No description defined

    Statements

    Defining formula
    ∑ j = a n - 1 ( - 1 ) j ⁢ f ⁢ ( j + h ) = 1 2 ⁢ ∑ k = 0 m - 1 E k ⁡ ( h ) k ! ⁢ ( ( - 1 ) n - 1 ⁢ f ( k ) ⁢ ( n ) + ( - 1 ) a ⁢ f ( k ) ⁢ ( a ) ) + R m ⁢ ( n ) , superscript subscript 𝑗 𝑎 𝑛 1 superscript 1 𝑗 𝑓 𝑗 ℎ 1 2 superscript subscript 𝑘 0 𝑚 1 Euler-polynomial-E 𝑘 ℎ 𝑘 superscript 1 𝑛 1 superscript 𝑓 𝑘 𝑛 superscript 1 𝑎 superscript 𝑓 𝑘 𝑎 subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle\sum_{j=a}^{n-1}(-1)^{j}f(j+h)=\frac{1}{2}\sum_{k=% 0}^{m-1}\frac{E_{k}\left(h\right)}{k!}\left((-1)^{n-1}f^{(k)}(n)+(-1)^{a}f^{(k% )}(a)\right)+R_{m}(n),}}
    0 references
    DLMF id
    DLMF:24.17.E1
    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
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1dec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1dec
    0 references
    Q12115
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1dec
    0 references
    Q12141
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C24.S17.XMD1.m1dec
    0 references
    Q12142
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C24.S17.XMD2.m1dec
    0 references
    Q12143
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S17.XMD3.m1dec
    0 references
    Q12144
    Defining formula
    f ( m ) ⁢ ( x ) superscript 𝑓 𝑚 𝑥 {\displaystyle{\displaystyle f^{(m)}(x)}}
    xml-id
    C24.S17.XMD4.m1dec
    0 references
    Q12145
    Defining formula
    R m ⁢ ( n ) subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle R_{m}(n)}}
    xml-id
    C24.S17.XMD5.m1dec
    0 references
     
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