We derive asymptotic expansions for the Stirling numbers of real arguments as defined by Flajolet and Prodinger. We also generalize certain classical identities for Stirling numbers with integral arguments to real or complex arguments.
Stirling numbers for complex arguments: asymptotics and identities / KEMKES G.; LEE C. F.; D. MERLINI; RICHMOND B.. - In: SIAM JOURNAL ON DISCRETE MATHEMATICS. - ISSN 0895-4801. - STAMPA. - 16:(2003), pp. 179-191. [10.1137/S0895480102401119]
Stirling numbers for complex arguments: asymptotics and identities
MERLINI, DONATELLA;
2003
Abstract
We derive asymptotic expansions for the Stirling numbers of real arguments as defined by Flajolet and Prodinger. We also generalize certain classical identities for Stirling numbers with integral arguments to real or complex arguments.
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