DLMF:6.14.E3 (Q2301): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1abdec
Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
test:

si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}

\shiftsinint@{\NVar{z}}
Property / Symbols used: sine integral / qualifier
 
xml-id: C6.S2.E10.m2adec

Latest revision as of 00:33, 2 January 2020

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DLMF:6.14.E3
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    Statements

    test
    ∫ 0 ∞ e - a ⁢ t ⁢ si ⁡ ( t ) ⁢ d t = - 1 a ⁢ arctan ⁡ a , superscript subscript 0 superscript 𝑒 𝑎 𝑡 shifted-sine-integral 𝑡 𝑡 1 𝑎 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathrm{si}\left(t\right)% \mathrm{d}t=-\frac{1}{a}\operatorname{arctan}a,}}
    0 references
    DLMF id
    DLMF:6.14.E3
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    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
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q10816
    test
    arctan ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}
    xml-id
    C4.S23.SS2.p1.m7adec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1abdec
    0 references
    sine integral
    test
    si ⁡ ( z ) shifted-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{si}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E10.m2adec
    0 references
     
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