DLMF:24.16.E2 (Q7571): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12135 / rank
 
Normal rank
Property / Symbols used: Q12135 / qualifier
 
Defining formula:

E n ( ℓ ) ⁡ ( x ) generalized-Euler-polynomial-E ℓ 𝑛 𝑥 {\displaystyle{\displaystyle E^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}

\genEulerpolyE{\NVar{\ell}}{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q12135 / qualifier
 
xml-id: C24.S16.Px1.p1.m4adec
Property / Symbols used
 
Property / Symbols used: Q12122 / rank
 
Normal rank
Property / Symbols used: Q12122 / qualifier
 
Defining formula:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q12122 / qualifier
 
xml-id: C24.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1adec
Property / Symbols used
 
Property / Symbols used: Q12111 / rank
 
Normal rank
Property / Symbols used: Q12111 / qualifier
 
Defining formula:

t 𝑡 {\displaystyle{\displaystyle t}}

t
Property / Symbols used: Q12111 / qualifier
 
xml-id: C24.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q12112 / rank
 
Normal rank
Property / Symbols used: Q12112 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12112 / qualifier
 
xml-id: C24.S1.XMD7.m1adec

Latest revision as of 01:50, 2 January 2020

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DLMF:24.16.E2
No description defined

    Statements

    Defining formula
    ( 2 e t + 1 ) ℓ ⁢ e x ⁢ t = ∑ n = 0 ∞ E n ( ℓ ) ⁡ ( x ) ⁢ t n n ! , superscript 2 superscript 𝑒 𝑡 1 ℓ superscript 𝑒 𝑥 𝑡 superscript subscript 𝑛 0 generalized-Euler-polynomial-E ℓ 𝑛 𝑥 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\left(\frac{2}{e^{t}+1}\right)^{\ell}e^{xt}=\sum_{% n=0}^{\infty}E^{(\ell)}_{n}\left(x\right)\frac{t^{n}}{n!},}}
    0 references
    DLMF id
    DLMF:24.16.E2
    0 references
    constraint
    | t | < π 𝑡 𝜋 {\displaystyle{\displaystyle|t|<\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q12135
    Defining formula
    E n ( ℓ ) ⁡ ( x ) generalized-Euler-polynomial-E ℓ 𝑛 𝑥 {\displaystyle{\displaystyle E^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S16.Px1.p1.m4adec
    0 references
    Q12122
    Defining formula
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C24.S1.XMD3.m1adec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1adec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1adec
    0 references
    Q12112
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1adec
    0 references
     
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