Difference between revisions of "Bessel Y"
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File:Bessel y plot.png|Graph of $Y_0,Y_1,\ldots,Y_5$ on $[0,20]$. | File:Bessel y plot.png|Graph of $Y_0,Y_1,\ldots,Y_5$ on $[0,20]$. | ||
| − | File: | + | File:Complexbessely,n=0.png|[[Domain coloring]] of $Y_0$. |
File:Domcolbesselysub1.png|[[Domain coloring]] of $Y_1(z)$. | File:Domcolbesselysub1.png|[[Domain coloring]] of $Y_1(z)$. | ||
File:Page 359Abramowitz-Stegun(Bessel functions).jpg|Bessel functions from [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/ Abramowitz&Stegun] | File:Page 359Abramowitz-Stegun(Bessel functions).jpg|Bessel functions from [http://dualaud.net/specialfunctionswiki/abramowitz_and_stegun-1.03/ Abramowitz&Stegun] | ||
Revision as of 20:06, 9 June 2016
Bessel functions of the second kind $Y_{\nu}$ are defined via the formula $$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$ Sometimes these functions are called Neumann functions and have the notation $N_{\nu}$ instead of $Y_{\nu}$.
Graph of $Y_0,Y_1,\ldots,Y_5$ on $[0,20]$.
Domain coloring of $Y_0$.
Domain coloring of $Y_1(z)$.
Bessel functions from Abramowitz&Stegun
.jpg)
Properties
References
Bessel's functions of the second order - C.V. Coates
