DLMF:4.9.E4 (Q1614): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec
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.m5adec
Property / Symbols used
 
Property / Symbols used: Q11223 / rank
 
Normal rank
Property / Symbols used: Q11223 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11223 / qualifier
 
xml-id: C4.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1cdec
Property / Symbols used
 
Property / Symbols used: expansion of exponential (locally) / rank
 
Normal rank
Property / Symbols used: expansion of exponential (locally) / qualifier
 
Defining formula:

e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}

e_{n}(z)
Property / Symbols used: expansion of exponential (locally) / qualifier
 
xml-id: C4.S9.XMD1.m1dec

Latest revision as of 18:13, 1 January 2020

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English
DLMF:4.9.E4
No description defined

    Statements

    Defining formula
    e z - e n - 1 ⁢ ( z ) = z n n ! - n ! ⁢ z ( n + 1 ) + z ( n + 2 ) - ( n + 1 ) ⁢ z ( n + 3 ) + 2 ⁢ z ( n + 4 ) - ⁢ ( n + 2 ) ⁢ z ( n + 5 ) + 3 ⁢ z ( n + 6 ) - ⁢ ⋯ , superscript 𝑒 𝑧 subscript 𝑒 𝑛 1 𝑧 continued-fraction superscript 𝑧 𝑛 𝑛 continued-fraction 𝑛 𝑧 𝑛 1 continued-fraction 𝑧 𝑛 2 continued-fraction 𝑛 1 𝑧 𝑛 3 continued-fraction 2 𝑧 limit-from 𝑛 4 continued-fraction 𝑛 2 𝑧 𝑛 5 continued-fraction 3 𝑧 limit-from 𝑛 6 ⋯ {\displaystyle{\displaystyle e^{z}-e_{n-1}(z)={\cfrac{z^{n}}{n!-\cfrac{n!z}{(n% +1)+\cfrac{z}{(n+2)-\cfrac{(n+1)z}{(n+3)+\cfrac{2z}{(n+4)-}}}}}\cfrac{(n+2)z}{% (n+5)+\cfrac{3z}{(n+6)-}}\cdots},}}
    0 references
    DLMF id
    DLMF:4.9.E4
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    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.m5adec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1adec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1cdec
    0 references
    expansion of exponential (locally)
    Defining formula
    e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}
    xml-id
    C4.S9.XMD1.m1dec
    0 references
     
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