DLMF:6.6.E3 (Q2250): Difference between revisions

From DRMF
Jump to navigation Jump to search
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: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1bdec

Latest revision as of 01:25, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:6.6.E3
No description defined

    Statements

    E 1 ( z ) = - ln z + e - z n = 0 z n n ! ψ ( n + 1 ) , exponential-integral 𝑧 𝑧 superscript 𝑒 𝑧 superscript subscript 𝑛 0 superscript 𝑧 𝑛 𝑛 digamma 𝑛 1 {\displaystyle{\displaystyle E_{1}\left(z\right)=-\ln z+e^{-z}\sum_{n=0}^{% \infty}\frac{z^{n}}{n!}\psi\left(n+1\right),}}
    0 references
    DLMF:6.6.E3
    0 references
    ψ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    C5.S2.E2.m2adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    E 1 ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    C6.S2.E1.m2aadec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2abdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C6.S1.XMD2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C6.S1.XMD3.m1bdec
    0 references