Difference between revisions of "Bessel Y"

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Bessel functions of the second kind $Y_{\nu}$ are defined via the formula
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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 $Y_{\nu}$.
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=Properties=
 
=Properties=
 
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[[Derivative of Bessel Y with respect to its order]]
  
 
=References=
 
=References=
* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Hankel H (1)}}: 9.1.3
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=findme|next=Hankel H (1)}}: 9.1.2
 
[http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=PPN600494829_0021%7CLOG_0023 Bessel's functions of the second order - C.V. Coates]<br />
 
[http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=PPN600494829_0021%7CLOG_0023 Bessel's functions of the second order - C.V. Coates]<br />
  

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 $Y_{\nu}$.


Properties

Derivative of Bessel Y with respect to its order

References

Bessel's functions of the second order - C.V. Coates

Bessel functions