A104996 Numerators of coefficients in a series solution to a certain differential equation.

1, -3, -5, -193, -13397, -315629, -282682949, -71668311457, -24436072994261, -829687356768133, -5984214162917084933, -4076572731127688098561, -669050282555409820416913, -3254803666762108782733299553, -3704926048371364507765541554757, -975581171350361622823383714646061

Offset: 1

Author

Zak Seidov, Mar 31 2005

Keywords

• sign
• frac

Comments

Serial solution of o.d.e. (A. Gruzinov, 2005): cos(t)*f'(t) + sin(t)*f''(t) + (3/4)*sin(t)*f(t) = 0, f(-Pi/2) = 1, f'(-Pi/2) = 0, f(t) = 1 - (3/8)*(t + Pi/2)^2 - (5/128)*(t + Pi/2)^4 - (193/15360)*(t + Pi/2)^4 - ... All coefficients (except for 1) are negative, and there is no simple recursion or other formula for the serial coefficients.

Links

• Andrei Gruzinov, Power of an axisymmetric pulsar, Physical Review Letters, Vol. 94, No. 2 (2005), 021101; arXiv preprint, arXiv:astro-ph/0407279, 2004.

Crossrefs

Cf. A104997 (denominators).

Programs

Mathematica

CoefficientList[Series[Hypergeometric2F1[-1/4, 3/4, 1/2, Sin[x]^2], {x, 0, 30}], x][[1 ;; -1 ;; 2]] // Numerator (* Amiram Eldar, Apr 29 2023 *)

Extensions

More terms from Amiram Eldar, Apr 29 2023