DLMF:2.3.E4 (Q720): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(8 intermediate revisions by the same user not shown)
Property / constraint
 

x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}

x\to+\infty
Property / constraint: x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
test:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11aadec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10945 / rank
 
Normal rank
Property / Symbols used: Q10945 / qualifier
 
test:

q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}

q(t)
Property / Symbols used: Q10945 / qualifier
 
xml-id: C2.S3.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q10947 / rank
 
Normal rank
Property / Symbols used: Q10947 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q10947 / qualifier
 
xml-id: C2.S3.XMD4.m1dec
Property / Symbols used
 
Property / Symbols used: Q10948 / rank
 
Normal rank
Property / Symbols used: Q10948 / qualifier
 
test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q10948 / qualifier
 
xml-id: C2.S3.XMD5.m1dec

Latest revision as of 15:50, 1 January 2020

No description defined
Language Label Description Also known as
English
DLMF:2.3.E4
No description defined

    Statements

    test
    ∫ a b e i ⁢ x ⁢ t ⁢ q ⁢ ( t ) ⁢ d t ∼ e i ⁢ a ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( a ) ⁢ ( i x ) s + 1 - e i ⁢ b ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( b ) ⁢ ( i x ) s + 1 , asymptotic-expansion superscript subscript 𝑎 𝑏 superscript 𝑒 𝑖 𝑥 𝑡 𝑞 𝑡 𝑡 superscript 𝑒 𝑖 𝑎 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑎 superscript 𝑖 𝑥 𝑠 1 superscript 𝑒 𝑖 𝑏 𝑥 superscript subscript 𝑠 0 superscript 𝑞 𝑠 𝑏 superscript 𝑖 𝑥 𝑠 1 {\displaystyle{\displaystyle\int_{a}^{b}e^{ixt}q(t)\mathrm{d}t\sim e^{iax}\sum% _{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1}-e^{ibx}\sum_{s=0}^{% \infty}q^{(s)}(b)\left(\frac{i}{x}\right)^{s+1},}}
    0 references
    DLMF id
    DLMF:2.3.E4
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
    0 references
    Symbols used
    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10945
    test
    q ⁢ ( t ) 𝑞 𝑡 {\displaystyle{\displaystyle q(t)}}
    xml-id
    C2.S3.XMD1.m1cdec
    0 references
    Q10947
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C2.S3.XMD4.m1dec
    0 references
    Q10948
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C2.S3.XMD5.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q720&oldid=3873"