Approximation of the longest common subsequence length for two long random strings

The expected value of the longest common subsequence of letters in two random words is considered as a function of the = A of alphabet and of words lengths and 𝑛. It is assumed that each letter independently appears at any position with equal probability. An approximate analitic expression for 𝐸(𝛼, 𝑚, 𝑛) calculation is presented that allow to calculate the 𝐸(𝑚, 𝑛, 𝛼) with an accuracy of 0.3 percent for 64 6 𝑚+𝑛 6 65, 536 and 1