DLMF:2.3.E5 (Q721): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec

Revision as of 16:50, 1 January 2020

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DLMF:2.3.E5
No description defined

    Statements

    Defining formula
    ∫ a ∞ e i ⁢ x ⁢ t ⁢ q ⁢ ( t ) ⁢ d t ∼ e i ⁢ a ⁢ x ⁢ ∑ s = 0 ∞ q ( s ) ⁢ ( a ) ⁢ ( i x ) s + 1 , asymptotic-expansion superscript subscript 𝑎 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 {\displaystyle{\displaystyle\int_{a}^{\infty}e^{ixt}q(t)\mathrm{d}t\sim e^{iax% }\sum_{s=0}^{\infty}q^{(s)}(a)\left(\frac{i}{x}\right)^{s+1},}}
    0 references
    DLMF id
    DLMF:2.3.E5
    0 references
    constraint
    x → + ∞ → 𝑥 {\displaystyle{\displaystyle x\to+\infty}}
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
     
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