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

Abstract

We present the explicit non‐recursive formulas for the Taylor series expansion coefficients for the functions S_n (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 S_n (t) Teiloro eilute koeficientu išreikštines formules. Jos yra nerekursyvine.

Key words:

• Emden ‐ Fowler equations
• Taylor series expansion
• lemniscatic sine