DLMF:6.12.E7 (Q2295): Difference between revisions

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Property / Symbols defined
 
Property / Symbols defined: remainder term (locally) / rank
 
Normal rank
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.m1adec
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: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: auxiliary function for sine and cosine integrals / rank
 
Normal rank
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
test:

f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}

\auxsincosintf@{\NVar{z}}
Property / Symbols used: auxiliary function for sine and cosine integrals / qualifier
 
xml-id: C6.S2.E17.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1edec
Property / Symbols used
 
Property / Symbols used: Q11308 / rank
 
Normal rank
Property / Symbols used: Q11308 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11308 / qualifier
 
xml-id: C6.S1.XMD3.m1bdec

Latest revision as of 00:32, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:6.12.E7
No description defined

    Statements

    test
    R n ( f ) ⁢ ( z ) = ( - 1 ) n ⁢ ∫ 0 ∞ e - z ⁢ t ⁢ t 2 ⁢ n t 2 + 1 ⁢ d t , superscript subscript 𝑅 𝑛 sine-cosine-integral-f 𝑧 superscript 1 𝑛 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 2 𝑛 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle R_{n}^{(\mathrm{f})}(z)=(-1)^{n}\int_{0}^{\infty}% \frac{e^{-zt}t^{2n}}{t^{2}+1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.12.E7
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    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.m3adec
    0 references
    auxiliary function for sine and cosine integrals
    test
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2abdec
    0 references
    Q11305
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1edec
    0 references
    Q11308
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C6.S1.XMD3.m1bdec
    0 references
     
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