Загрузка данных
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% Ссылка на источник.
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% Номер группы формул.
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\begin{document}
% Верхний колонтитул.
\noindent
\makebox[\textwidth][s]{%
{\sffamily\bfseries\small 656}%
\hfill
{\sffamily\small Гамма-функция и родственные ей функции}%
\hfill
{\sffamily\bfseries\small 6.324}%
}
\par
\vspace{-1.5mm}
\hrule height 0.6pt
\vspace{0.7mm}
\hrule height 0.6pt
\vspace{6mm}
% Продолжение предыдущей группы.
\begin{tabular}{@{}p{1cm}p{11.7cm}p{3.3cm}@{}}
\hspace*{0.23cm}2.
&
$\displaystyle
\int_0^\infty
C\left(\sqrt{t}\right)e^{-pt}\,dt
=
\frac{
\left(\sqrt{p^2+1}+p\right)^{\frac12}
}{
2p\sqrt{p^2+1}
}
$
&
\raggedleft\arraybackslash
\source{ЭД 122(58)и}
\end{tabular}
% ------------------------------------------------------------
\groupnumber{6.324}
\begin{tabular}{@{}p{1cm}p{8.7cm}p{3cm}p{3.3cm}@{}}
\hspace*{0.23cm}1.
&
$\displaystyle
\int_0^\infty
\left[\frac12-S(x)\right]\sin 2px\,dx
=
\frac{1+\sin p^2-\cos p^2}{4p}
$
&
$\displaystyle [p>0]$
&
\raggedleft\arraybackslash
\source{Ни2 61(12)и}
\\[5mm]
\hspace*{0.23cm}2.
&
$\displaystyle
\int_0^\infty
\left[\frac12-C(x)\right]\sin 2px\,dx
=
\frac{1-\sin p^2-\cos p^2}{4p}
$
&
$\displaystyle [p>0]$
&
\raggedleft\arraybackslash
\source{Ни2 61(11)и}
\end{tabular}
% ------------------------------------------------------------
\groupnumber{6.325}
\begin{tabular}{@{}p{1cm}p{3.2cm}p{5.5cm}p{3cm}p{3.3cm}@{}}
\hspace*{0.23cm}1.
&
$\displaystyle
\int_0^\infty S(x)\sin b^2x^2\,dx
$
&
$\displaystyle
=\frac{\sqrt{\pi}}{b}\,2^{-\frac52}
$
&
$\displaystyle [0<b^2<1]$
&
\\[3mm]
&
&
$\displaystyle =0$
&
$\displaystyle [b^2>1]$
&
\\[1mm]
\multicolumn{5}{@{}r@{}}{\source{БЭ1 I 98(21)и}}
\\[6mm]
\hspace*{0.23cm}2.
&
$\displaystyle
\int_0^\infty C(x)\cos b^2x^2\,dx
$
&
$\displaystyle
=\frac{\sqrt{\pi}}{b}\,2^{-\frac52}
$
&
$\displaystyle [0<b^2<1]$
&
\\[3mm]
&
&
$\displaystyle =0$
&
$\displaystyle [b^2>1]$
&
\\[1mm]
\multicolumn{5}{@{}r@{}}{\source{БЭ1 I 42(22)}}
\end{tabular}
% ------------------------------------------------------------
\groupnumber{6.326}
\begin{tabular}{@{}p{1cm}p{15cm}@{}}
\hspace*{0.23cm}1.
&
$\displaystyle
\int_0^\infty
\left[\frac12-S(x)\right]\si(2px)\,dx
=
\left(\frac{\pi}{8}\right)^{1/2}
\bigl(S(p)+C(p)-1\bigr)
-
\frac{1+\sin p^2-\cos p^2}{4p}
$
\\[2mm]
&
\hspace*{8.7cm}%
$\displaystyle [p>0]$
\hfill
\source{Ни2 61(15)и}
\\[5mm]
\hspace*{0.23cm}2.
&
$\displaystyle
\int_0^\infty
\left[\frac12-C(x)\right]\si(2px)\,dx
=
\left(\frac{\pi}{8}\right)^{1/2}
\bigl(S(p)-C(p)\bigr)
-
\frac{1-\sin p^2-\cos p^2}{4p}
$
\\[2mm]
&
\hspace*{8.7cm}%
$\displaystyle [p>0]$
\hfill
\source{Ни2 61(14)и}
\end{tabular}
% ------------------------------------------------------------
\par\vspace{7mm}
{\Large\sffamily\bfseries
6.4 Гамма-функция и родственные ей функции
}
\par\vspace{4mm}
{\large\sffamily\bfseries
6.41 Гамма-функция
}
\par\vspace{3mm}
\begin{tabular}{@{}p{1.45cm}p{14.55cm}@{}}
{\bfseries 6.411}\textsuperscript{11}
&
$\displaystyle
\int_{-\infty}^{\infty}
\Gamma(\alpha+x)\,\Gamma(\beta-x)\,dx
=
-i\pi\,2^{1-\alpha-\beta}\,\Gamma(\alpha+\beta)
$
\\[2mm]
&
\hfill
{\small
$\bigl[
\operatorname{Re}(\alpha+\beta)<1
\text{ и либо }
\operatorname{Im}\alpha<0<\operatorname{Im}\beta,
\text{ либо }
\operatorname{Im}\beta<0<\operatorname{Im}\alpha
\bigr]$
}
\\[0.5mm]
&
\hfill\source{БЭ1 II 297(1)}
\\[5mm]
&
\hspace*{3.8cm}%
$\displaystyle
=i\pi\,2^{1-\alpha-\beta}\,\Gamma(\alpha+\beta)
$
\\[2mm]
&
\hfill
$\bigl[
\operatorname{Re}(\alpha+\beta)<1,\quad
\operatorname{Im}\alpha<0,\quad
\operatorname{Im}\beta<0
\bigr]$
\\[0.5mm]
&
\hfill\source{БЭ1 II 297(2)}
\\[5mm]
&
\hspace*{3.8cm}%
$\displaystyle =0$
\\[2mm]
&
\hfill
$\bigl[
\operatorname{Re}(\alpha+\beta)<1,\quad
\operatorname{Im}\alpha>0,\quad
\operatorname{Im}\beta>0
\bigr]$
\\[0.5mm]
&
\hfill\source{БЭ1 II 297(3)}
\end{tabular}
\end{document}