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Display information for equation id:math.3061.9 on revision:3061

* Page found: Nakajima-Zwanzig-Gleichung (eq math.3061.9)

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Hash: a3b58660046ab6f158000ec0f4d2f8d0

TeX (original user input):

{{\text{d}}_{t}}\mathcal{P}\chi =\mathcal{P}L\mathcal{P}\chi +\underbrace{\mathcal{P}L{{e}^{\mathcal{Q}Lt}}Q\chi (t=0)}_{=0}+\int\limits_{0}^{t}{dt'\mathcal{K}({t}')\mathcal{P}\chi (t-{t}')|}

TeX (checked):

{{\text{d}}_{t}}{\mathcal {P}}\chi ={\mathcal {P}}L{\mathcal {P}}\chi +\underbrace {{\mathcal {P}}L{{e}^{{\mathcal {Q}}Lt}}Q\chi (t=0)} _{=0}+\int \limits _{0}^{t}{dt'{\mathcal {K}}({t}'){\mathcal {P}}\chi (t-{t}')|}

LaTeXML (experimental; uses MathML) rendering

MathML (12.285 KB / 1.951 KB) :

{\displaystyle{\displaystyle{{\text{d}}_{t}}\mathcal{P}\chi=\mathcal{P}L% \mathcal{P}\chi+\underbrace{\mathcal{P}L{{e}^{\mathcal{Q}Lt}}Q\chi(t=0)}_{=0}+% \int\limits_{0}^{t}{dt^{\prime}\mathcal{K}({t}^{\prime})\mathcal{P}\chi(t-{t}^% {\prime})|}}}

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{{\text{d}}_{t}}{\mathcal {P}}\chi ={\mathcal {P}}L{\mathcal {P}}\chi +\underbrace {{\mathcal {P}}L{{e}^{{\mathcal {Q}}Lt}}Q\chi (t=0)} _{=0}+\int \limits _{0}^{t}{dt'{\mathcal {K}}({t}'){\mathcal {P}}\chi (t-{t}')|}

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        <mi>&#x03C7;<!-- χ --></mi>
        <mo>=</mo>
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            <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi>
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            <mi class="MJX-tex-caligraphic" mathvariant="script">P</mi>
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        <mi>&#x03C7;<!-- χ --></mi>
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                      <mi>L</mi>
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                <mi>Q</mi>
                <mi>&#x03C7;<!-- χ --></mi>
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                <mi>t</mi>
                <mo>=</mo>
                <mn>0</mn>
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            <mrow class="MJX-TeXAtom-ORD">
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          <mi>&#x03C7;<!-- χ --></mi>
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          <mi>t</mi>
          <mo>&#x2212;<!-- − --></mo>
          <msup>
            <mrow class="MJX-TeXAtom-ORD">
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    <annotation encoding="application/x-tex">{\displaystyle {{\text{d}}_{t}}{\mathcal {P}}\chi ={\mathcal {P}}L{\mathcal {P}}\chi +\underbrace {{\mathcal {P}}L{{e}^{{\mathcal {Q}}Lt}}Q\chi (t=0)} _{=0}+\int \limits _{0}^{t}{dt'{\mathcal {K}}({t}'){\mathcal {P}}\chi (t-{t}')|}}</annotation>
  </semantics>
</math>

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$t$

${\mathcal {P}}$

$\chi$

${\mathcal {P}}$

$L$

${\mathcal {P}}$

$\chi$

${\mathcal {P}}$

$L$

$e$

${\mathcal {Q}}$

$L$

$t$

$Q$

$\chi$

$t$

$t$

$t'$

${\mathcal {K}}$

$t'$

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