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The coefficient problem had been extensively investigated, and it is known that |a_n| <= 2/e for n=1,2,3, and 4. That this inequality may hold for n in N, is know as the Kry\\.z conjecture. It turns out that for f in B-tilde with a_0 = e^-t,\n  f(z) << e^{-t (1+z)/(1-z)}\n so that the superordinate functions e^{-t (1+z)/(1-z)} = sum F_k(t) z^k are of special interest. 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