Difference between revisions of "Bessel Y"
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Bessel functions (of the second kind) $Y_{\nu}$ are defined via the formula | Bessel functions (of the second kind) $Y_{\nu}$ are defined via the formula | ||
$$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$ | $$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$ | ||
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| + | <div align="center"> | ||
| + | <gallery> | ||
| + | File:Bessel y plot.png|Graph of $Y_0,Y_1,\ldots,Y_5$ on $[0,20]$. | ||
| + | File:Complex bessel y sub 0.png|[[Domain coloring]] of [[analytic continuation]] of $Y_0(z)$. | ||
| + | </gallery> | ||
| + | </div> | ||
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=Properties= | =Properties= | ||
Revision as of 23:35, 19 May 2015
Bessel functions (of the second kind) $Y_{\nu}$ are defined via the formula $$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$
Graph of $Y_0,Y_1,\ldots,Y_5$ on $[0,20]$.
Domain coloring of analytic continuation of $Y_0(z)$.
