Originally he found that (1) is satisfied by A 2 4 e -~ and later in a paper written with VE~A T. SOs [4] it is shown that A = 2el+4/~ too, satisfies the inequality (1). They remark that the lessening of the constant A plays an important role at certain applications and the question was raised to find the least numerical constant A* for which M ~ , n > ~ ..... (A) independently of m and n. Applying an idea of P. ERD6S they showed [4] that A*>1,321 and in the same paper they indicated a way which it was expected to lead to a better lower estimation of A*. They have shown, namely, that if m,,(y) is the Hermite polynomial defined by