Timeline for Orthogonality with Bessel functions of rational order
Current License: CC BY-SA 3.0
5 events
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| Apr 3, 2017 at 20:45 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Apr 3, 2017 at 14:35 | comment | added | Francois Ziegler | @user135626 Rather the opposite: if $\mu, \nu$ have common denominator $N>1$ (e.g. $\mu=0$, $\smash{\nu=\frac12}$), then $\smash{\int_0^b e^{i(\nu-\mu)\phi}d\phi=0}$ generally requires $b$ to be a multiple of $2N\pi$, not just $2\pi$, i.e. you must expand the domain to an $N$-fold cover of the circle. | |
| Apr 3, 2017 at 11:57 | comment | added | user135626 | If we could ignore or avoid the angular multi-valuedness for a moment (e.g. by limiting the chosen domains of $\phi$ in practice), would the product itself be orthogonal for different values of $v$ when $v=M/N$? | |
| Apr 3, 2017 at 5:28 | history | edited | Francois Ziegler | CC BY-SA 3.0 |
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| Apr 3, 2017 at 5:00 | history | answered | Francois Ziegler | CC BY-SA 3.0 |