DLMF:4.9.E4 (Q1614)

From DRMF
Revision as of 18:13, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1614&oldid=26883"