DLMF:4.26.E12 (Q1828)

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DLMF:4.26.E12
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ sin ⁡ ( m ⁢ t ) t ⁢ d t = { 1 2 ⁢ π , m > 0 , 0 , m = 0 , - 1 2 ⁢ π , m < 0 . superscript subscript 0 𝑚 𝑡 𝑡 𝑡 cases 1 2 𝜋 𝑚 0 0 𝑚 0 1 2 𝜋 𝑚 0 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\sin\left(mt\right)}{t}% \mathrm{d}t=\begin{cases}\frac{1}{2}\pi,&m>0,\\ 0,&m=0,\\ -\frac{1}{2}\pi,&m<0.\end{cases}}}
    0 references
    DLMF id
    DLMF:4.26.E12
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
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    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2agdec
    0 references
    Q11249
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C4.S1.XMD2.m1bdec
    0 references
     
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