Bounds on the entropy series

Upper bounds on the entropy of a countable integer-valued random variable are furnished in terms of the expectation of the logarithm function. In particular, an upper bound is derived that is sharper than that of P. Elias (ibid., vol.IT-21, no.2, p.194-203, 1975), for all values of E/sub p/(log). Bounds that are better only for large values of E/sub p/ than the previous known upper bounds are also provided.<
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