Difference between revisions of "Derivative of Bessel Y with respect to its order"
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| − | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Derivative of Bessel J with respect to its order|next=findme}}: 9.1.65 | + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Derivative of Bessel J with respect to its order|next=findme}}: $9.1.65$ |
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| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 00:50, 28 August 2016
Theorem
The following formula holds for $\nu \neq 0, \pm 1, \pm 2, \ldots$: $$\dfrac{\partial}{\partial \nu} Y_{\nu}(z)=\cot(\nu \pi) \left[ \dfrac{\partial}{\partial \nu} J_{\nu}(z)-\pi Y_{\nu}(z) \right] - \csc(\nu \pi) \dfrac{\partial}{\partial \nu} J_{-\nu}(z)-\pi J_{\nu}(z),$$ where $Y_{\nu}$ denotes the Bessel function of the second kind, $\cot$ denotes the cotangent, $J_{\nu}$ denotes the Bessel function of the first kind, $\pi$ denotes pi, and $\csc$ denotes the cosecant.
Proof
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): $9.1.65$
