A104241 Decimal expansion of the first zero of the solution to the differential equation cos(t)*f'(t) + sin(t)*f''(t) + (3/4)*sin(t)*f(t) = 0, f(-Pi/2) = 1, f'(-Pi/2) = 0 (negated).
2, 2, 2, 0, 5, 6, 5, 6, 6, 7, 4, 7, 5, 8, 0, 6, 0, 9, 1, 8, 6, 1, 9, 9, 2, 1, 2, 9, 3, 3, 7, 6, 3, 3, 4, 6, 9, 7, 9, 4, 1, 7, 6, 1, 6, 3, 3, 9, 1, 2, 6, 4, 1, 5, 6, 1, 7, 2, 2, 1, 0, 7, 8, 7, 1, 6, 1, 4, 7, 9, 4, 5, 0, 6, 0, 2, 5, 5, 1, 5, 7, 6, 7, 8, 6, 0, 6, 7, 2, 2, 5, 4, 3, 9, 4, 0, 5, 2, 2, 3, 3, 4, 5, 2, 9
Offset: 0
Links
- Andrei Gruzinov, Power of an axisymmetric pulsar, Physical Review Letters, Vol. 94, No. 2 (2005), 021101; arXiv preprint, arXiv:astro-ph/0407279, 2004.
Programs
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Mathematica
RealDigits[x /. FindRoot[Hypergeometric2F1[-1/4, 3/4, 1/2, Sin[x + Pi/2]^2], {x, -0.2}, WorkingPrecision -> 120], 10, 105][[1]] (* Amiram Eldar, Apr 29 2023 *)
Formula
-0.22205656674758060918619921293376334697941...
Extensions
Offset corrected by Michel Marcus, Nov 12 2019
a(53) corrected and more terms added by Amiram Eldar, Apr 29 2023