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We present two-sided estimates of moments and tails of polynomial chaoses oforder at most three generated by independent symmetric random variables withlog-concave tails as well as for chaoses of arbitrary order generated byindependent symmetric exponential variables. The estimates involve onlydeterministic quantities and are optimal up to constants depending only on theorder of the chaos variable.

Tail and moment estimates for chaoses generated by symmetric random variables with logarithmically concave tails