Exact Asymptotic Expansion of Singular Solutions for the (𝟐+1)-D Protter Problem

Table 1

The order of singularity of the solution and the functions 𝑊^{𝑛𝑘,𝑖}.

	𝑙	𝑙−1	𝑙−2	𝑙−3	⋯	𝑝		⋯	4	3	2
0	⋯	⋯	⋯	⋯	⋯	⋯		⋯	𝑊^42,𝑖	⋄	𝑊^21,𝑖
1	⋯	⋯	⋯	⋯	⋯	⋯		⋯	⋄	𝑊^31,𝑖	⋄
2	⋯	⋯	⋯	⋯	⋯	⋯		⋯	𝑊^41,𝑖	⋄	𝑊^20,𝑖
3	⋯	⋯	⋯	⋯	⋯	⋯		⋯	⋄	𝑊^30,𝑖
4	⋯	⋯	⋯	⋯	⋯	⋯		⋯	𝑊^40,𝑖
⋮	⋯	⋯	⋯	⋯	⋯	⋯		⋯
𝑝−2𝑞	⋯	⋯	⋯	⋯	⋯	𝑊^𝑝𝑞,𝑖	⋯
						⋯
⋮	⋯	⋯	⋯	⋯	⋯
𝑙−3	⋄	𝑊^𝑙−11,𝑖	⋄	𝑊^𝑙−30,𝑖
𝑙−2	𝑊^𝑙1,𝑖	⋄	𝑊^𝑙−20,𝑖
𝑙−1	⋄	𝑊^𝑙−10,𝑖
𝑙	𝑊^𝑙0,𝑖