A104997 Denominators of coefficients in a series solution to a certain differential equation.

1, 8, 128, 15360, 3440640, 247726080, 653996851200, 476109707673600, 457065319366656000, 43034457761906688000, 850360885375276154880000, 1571466916173510334218240000, 693959790182222163590774784000, 9021477272368888126680072192000000, 27280947271643517695080538308608000000

Offset: 1

Author

Zak Seidov, Mar 31 2005

Keywords

• nonn
• frac

Comments

Series 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 1) are negative, there is no simple recursion or other formula for the series coefficients.

Links

• Robert Israel, Table of n, a(n) for n = 1..203
• 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. A104996 (numerators).

Programs

Maple

de:= sin(s)*D(g)(s)-cos(s)*(D@@2)(g)(s)-3/4*cos(s)*g(s)=0:
S:= dsolve({de, g(0)=1, D(g)(0)=0},g(s), series, order=51):
seq(denom(coeff(rhs(S),s,2*j)),j=0..25); # Robert Israel, Jun 05 2019

Mathematica

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

Formula

The solution to the o.d.e. is hypergeom([-1/4,3/4],[1/2],sin(t+Pi/2)). - Robert Israel, Jun 05 2019

Extensions

More terms from Robert Israel, Jun 05 2019