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# Formelsammlung Mathematik: Bestimmte Integrale: Form R(x,sin,BesselJ)

Zurück zu Bestimmte Integrale

##### 2.1
${\displaystyle \int _{0}^{\infty }J_{0}(ax)\,\sin(cx)\,dx=\left\{{\begin{matrix}{\frac {1}{\sqrt {c^{2}-a^{2}}}}&ac\end{matrix}}\right.}$

##### 2.2
${\displaystyle \int _{0}^{\infty }J_{0}(ax)\,{\frac {\sin(cx)}{x}}\,dx=\left\{{\begin{matrix}{\frac {\pi }{2}}&ac\end{matrix}}\right.}$

##### 3.1
${\displaystyle \int _{0}^{\infty }J_{2n}(ax)\,{\frac {\sin(cx)}{x}}\,dx=\left\{{\begin{matrix}0&ac\end{matrix}}\right.}$

##### 3.2
${\displaystyle \int _{0}^{\infty }J_{2n+1}(ax)\,{\frac {\sin(cx)}{x}}\,dx=\left\{{\begin{matrix}{\frac {(-1)^{n}}{2n+1}}\left(T_{2n+1}\left({\frac {c}{a}}\right)-U_{2n}\left({\frac {c}{a}}\right)\,{\sqrt {\left({\frac {c}{a}}\right)^{2}-1}}\right)&ac\end{matrix}}\right.}$

##### 3.3
${\displaystyle \int _{0}^{\infty }J_{\nu }(ax)\,{\frac {\sin(cx)}{x}}\,dx=\left\{{\begin{matrix}{\frac {\sin \left(\nu \arcsin {\frac {c}{a}}\right)}{\nu }}&a>c\\\\{\frac {a^{\nu }\,\sin {\frac {\nu \pi }{2}}}{\nu \,\left(c+{\sqrt {c^{2}-a^{2}}}\right)^{\nu }}}&a-1}$