The Taylor series expansion coefficients for solutions of the Emden‐Fowler type equations

We present the explicit non‐recursive formulas for the Taylor series expansion coefficients for the functions Sn (t) defined as solutions of the Emden ‐ Fowler type equations x” = –nx 2n−1 with the initial conditions x(0) = 0, x‘(0) = 1, where n = 1,2,… Pateikiamos vadinamos Emdeno‐Faulerio lygties x” = –nx 2n−1 pradinio uždavinio x(0) = 0, x‘(0) = 1,(n = 1,2,…) sprendiniu Sn (t) Teiloro eilute koeficientu išreikštines formules. Jos yra nerekursyvine. First Published Online: 14 Oct 2010