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(m,n) =a f(m,n-1)+(1- a)f(m -1,n-1), | f(m,n)| < 1989

Source: 1989 ITAMO p6

January 31, 2020
functionrecurrence relationalgebra

Problem Statement

Given a real number α\alpha, a function ff is defined on pairs of nonnegative integers by f(0,0)=1,f(m,0)=f(0,m)=0f(0,0) = 1, f(m,0) = f(0,m) = 0 for m>0m > 0, f(m,n)=αf(m,n−1)+(1−α)f(m−1,n−1)f(m,n) = \alpha f(m,n-1)+(1- \alpha)f(m -1,n-1) for m,n>0m,n > 0. Find the values of α\alpha such that ∣f(m,n)∣<1989| f(m,n)| < 1989 holds for any integers m,n≥0m,n \ge 0.
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