Загрузка данных


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% Ссылка на источник.
\newcommand{\source}[1]{{\small\sffamily\bfseries #1}}

% Номер группы формул.
\newcommand{\groupnumber}[1]{%
    \par\vspace{4mm}%
    {\bfseries #1}\par
    \vspace{2mm}%
}

\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}