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 |
$$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$ | $$Y_{\nu}(z)=\dfrac{J_{\nu}(z)\cos(\nu \pi)-J_{-\nu}(z)}{\sin(\nu \pi)}.$$ | ||
Sometimes these functions are called Neumann functions and have the notation $N_{\nu}$ instead of $Y_{\nu}$. | Sometimes these functions are called Neumann functions and have the notation $N_{\nu}$ instead of $Y_{\nu}$. | ||
Latest revision as of 15:39, 10 July 2017
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 $Y_0$.
Graph of $Y_0,Y_1,Y_2$, and $Y_3$.
Domain coloring of $Y_0$.
Domain coloring of $Y_1$.
Bessel functions from Abramowitz&Stegun
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Properties
Derivative of Bessel Y with respect to its order
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 9.1.2
Bessel's functions of the second order - C.V. Coates
