cp's OEIS Frontend

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

%I A104997 #26 May 20 2023 23:17:24
%S A104997 1,8,128,15360,3440640,247726080,653996851200,476109707673600,
%T A104997 457065319366656000,43034457761906688000,850360885375276154880000,
%U A104997 1571466916173510334218240000,693959790182222163590774784000,9021477272368888126680072192000000,27280947271643517695080538308608000000
%N A104997 Denominators of coefficients in a series solution to a certain differential equation.
%C A104997 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.
%H A104997 Robert Israel, <a href="/A104997/b104997.txt">Table of n, a(n) for n = 1..203</a>
%H A104997 Andrei Gruzinov, <a href="https://doi.org/10.1103/PhysRevLett.94.021101">Power of an axisymmetric pulsar</a>, Physical Review Letters, Vol. 94, No. 2 (2005), 021101; <a href="https://arxiv.org/abs/astro-ph/0407279">arXiv preprint</a>, arXiv:astro-ph/0407279, 2004.
%F A104997 The solution to the o.d.e. is hypergeom([-1/4,3/4],[1/2],sin(t+Pi/2)). - _Robert Israel_, Jun 05 2019
%p A104997 de:= sin(s)*D(g)(s)-cos(s)*(D@@2)(g)(s)-3/4*cos(s)*g(s)=0:
%p A104997 S:= dsolve({de, g(0)=1, D(g)(0)=0},g(s), series, order=51):
%p A104997 seq(denom(coeff(rhs(S),s,2*j)),j=0..25); # _Robert Israel_, Jun 05 2019
%t A104997 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 *)
%Y A104997 Cf. A104996 (numerators).
%K A104997 nonn,frac
%O A104997 1,2
%A A104997 _Zak Seidov_, Mar 31 2005
%E A104997 More terms from _Robert Israel_, Jun 05 2019