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A245461 Decimal expansion of constant in the Rayleigh criterion: first zero of J_1, divided by Pi.

%I A245461 #39 Aug 21 2025 09:15:29
%S A245461 1,2,1,9,6,6,9,8,9,1,2,6,6,5,0,4,4,5,4,9,2,6,5,3,8,8,4,7,4,6,5,2,5,5,
%T A245461 1,7,7,8,7,9,3,5,9,3,3,0,7,7,5,1,1,2,1,2,9,4,5,6,3,8,1,2,6,5,5,7,6,9,
%U A245461 4,3,2,8,0,2,8,0,7,6,0,1,4,4,2,5,0,8,7
%N A245461 Decimal expansion of constant in the Rayleigh criterion: first zero of J_1, divided by Pi.
%C A245461 The angular resolution (diffraction limit), in radians, is this constant times the wavelength of the light used divided by the aperture diameter. That is: objects closer than this angle cannot be resolved as separate objects.
%C A245461 Note that the small angle approximation sin(theta) =~ theta can be used. Also, a commonly used approximation to this constant is 1.220. - _John W. Nicholson_, Jul 29 2014
%C A245461 For example, a radio telescope with a 300-meter aperture observing at the hydrogen line (21.106... cm) can distinguish objects at most 0.04916... degrees apart. - _Charles R Greathouse IV_, Mar 08 2018
%H A245461 Vincenzo Librandi, <a href="/A245461/b245461.txt">Table of n, a(n) for n = 1..10000</a>
%H A245461 COSMOS - The SAO Encyclopedia of Astronomy, <a href="http://astronomy.swin.edu.au/cosmos/R/Rayleigh+Criterion">Rayleigh Criterion</a>
%H A245461 Rene Kay, Todd Kay, <a href="https://hal.archives-ouvertes.fr/hal-02870885v2">Planet Seeker Interferometer (PSI)</a>, hal-02870885v2 [astro-ph.IM], 2020.
%H A245461 Wikipedia, <a href="http://en.wikipedia.org/wiki/Angular_resolution">Angular resolution</a>
%H A245461 Wikipedia, <a href="https://en.wikipedia.org/wiki/Diffraction-limited_system">Diffraction-limited system</a>
%H A245461 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A245461 Equals A115369/A000796.
%e A245461 1.21966989126650445492653884746525517787935933077511...
%t A245461 RealDigits[ BesselJZero[1, 1]/Pi, 10, 111][[1]] (* _Robert G. Wilson v_, Jul 23 2014 *)
%o A245461 (PARI) solve(x=3,4,besselj(1,x))/Pi
%o A245461 (PARI) besseljzero(1)/Pi \\ _Charles R Greathouse IV_, Aug 09 2022
%Y A245461 Cf. A115369, A221210.
%K A245461 nonn,cons
%O A245461 1,2
%A A245461 _Charles R Greathouse IV_, Jul 22 2014