Computation of the Added Masses of an Unconventional Airship

Table 1

Characteristics of lam’s functions of first kind.

Function	Principal product	𝑚	Number	Value of the index 𝑖
𝐾^𝑧𝑖𝑛(𝑥)	𝜓𝑛(𝑥)=𝑥^𝑛−2𝑘	𝑘	𝑘+1	𝑖=0,…,𝑘
𝐿^𝑧𝑖𝑛(𝑥)	𝜓𝑛(𝑥)=𝑥^1−𝑛+2𝑘|𝑥^2−𝑎^2|	𝑛−𝑘−1	𝑛−𝑘	𝑖=𝑘+1,…,𝑛
𝑀^𝑧𝑖𝑛(𝑥)	𝜓𝑛(𝑥)=𝑥^1−𝑛+2𝑘|𝑥^2−𝑏^2|	𝑛−𝑘−1	𝑛−𝑘	𝑖=𝑛+1,…,2𝑛−𝑘
𝑁^𝑧𝑖𝑛(𝑥)	𝜓𝑛(𝑥)=𝑥^𝑛−2𝑘|(𝑥^2−𝑎^2)(𝑥^2−𝑏^2)|	𝑘−1	𝑘	𝑖=2𝑛−𝑘+1,…,2𝑛

Total = 2𝑛+1.