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The generating function for restricted partitions is a finite product with aLaurent expansion at each root of unity. The question of the behavior of theseLaurent coefficients as the size of the product increases goes back toRademacher and his work on partitions. Building on the methods of Drmota,Gerhold and previous results of the author, we complete this description andgive the full asymptotic expansion of each coefficient at every root of unity.These techniques are also shown to give the asymptotics of Sylvester waves.

Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions