The authors derive explicit asymptotic series for 1/li_k(x) whose coefficients come from a combinatorial recurrence, generalizing Panaitopol's expansion from primes to prime k-tuples.
Comtet, Sur les coefficients de l’inverse de la s´ erie formelle ∑ n!xn, C
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Asymptotic expansions for the reciprocal Hardy-Littlewood logarithmic integrals
The authors derive explicit asymptotic series for 1/li_k(x) whose coefficients come from a combinatorial recurrence, generalizing Panaitopol's expansion from primes to prime k-tuples.