DLMF:7.19.E11 (Q2478): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1addec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aedec
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.m3addec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec

Latest revision as of 13:35, 2 January 2020

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DLMF:7.19.E11
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    Statements

    𝖵 ( u a , 1 4 a 2 ) = a 0 e - a t - 1 4 t 2 sin ( u t ) d t . Voigt-V 𝑢 𝑎 1 4 superscript 𝑎 2 𝑎 superscript subscript 0 superscript 𝑒 𝑎 𝑡 1 4 superscript 𝑡 2 𝑢 𝑡 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\frac{u}{a},\frac{1}{4a^{2}}\right% )=a\int_{0}^{\infty}e^{-at-\frac{1}{4}t^{2}}\sin\left(ut\right)\mathrm{d}t.}}
    0 references
    DLMF:7.19.E11
    0 references
    𝖵 ( x , t ) Voigt-V 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\NVar{x},\NVar{t}\right)}}
    C7.S19.E2.m2ahdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1addec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aedec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3addec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references