A Representation of the Exact Solution of Generalized Lane-Emden Equations Using a New Analytical Method

Table 2

The values of the residual error function Res^𝑘(𝑥) to Example 4 when 𝑘=10,15,20,25 for different values of 𝑥 in [0,2].

𝑥𝑖	Res^10(𝑥𝑖)	Res^15(𝑥𝑖)	Res^20(𝑥𝑖)	Res^25(𝑥𝑖)
0	0	0	0	0
0.1	4.528461×10^−13	4.528461×10^−13	4.528461×10^−13	4.528461×10^−13
0.2	1.250167×10^−12	3.996803×10^−15	3.996803×10^−15	3.996803×10^−15
0.5	1.785672×10^−9	6.611378×10^−14	1.045275×10^−13	1.045275×10^−13
1	3.539988×10^−6	8.587641×10^−9	4.061307×10^−12	1.395550×10^−13
1.5	2.884109×10^−4	3.208217×10^−6	1.902825×10^−8	1.854792×10^−10
2	6.215665×10^−3	1.865257×10^−4	7.253518×10^−6	1.909733×10^−7