DLMF:8.11.E13 (Q2586): 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
 
test:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ahdec
Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: functions (locally) / rank
 
Normal rank
Property / Symbols used: functions (locally) / qualifier
 
test:

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

e_{n}(z)
Property / Symbols used: functions (locally) / qualifier
 
xml-id: C8.S4.XMD1.m1dec

Latest revision as of 12:55, 2 January 2020

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DLMF:8.11.E13
No description defined

    Statements

    test
    lim n → ∞ ⁡ e n ⁢ ( n ⁢ x ) e n ⁢ x = { 0 , x > 1 , 1 2 , x = 1 , 1 , 0 ≤ x < 1 . subscript → 𝑛 subscript 𝑒 𝑛 𝑛 𝑥 superscript 𝑒 𝑛 𝑥 cases 0 𝑥 1 1 2 𝑥 1 1 0 𝑥 1 {\displaystyle{\displaystyle\lim_{n\to\infty}\frac{e_{n}(nx)}{e^{nx}}=\begin{% cases}0,&x>1,\\ \tfrac{1}{2},&x=1,\\ 1,&0\leq x<1.\end{cases}}}
    0 references
    DLMF id
    DLMF:8.11.E13
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ahdec
    0 references
    Q11332
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1ddec
    0 references
    Q11329
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1bdec
    0 references
    functions (locally)
    test
    e n ⁢ ( z ) subscript 𝑒 𝑛 𝑧 {\displaystyle{\displaystyle e_{n}(z)}}
    xml-id
    C8.S4.XMD1.m1dec
    0 references
     
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