On the asymptotics of products related to generalizations of the Wilf and Mortini problems. (English) Zbl 1350.33001
The authors determine the asymptotic expansions as \(n\to\infty\) of the products determined by \(P_n= \prod^n_{j=1} (1+ p_1/j+\cdots+ p_m/j^m)\) and \(Q_n= \prod^n_{j=1} (1+ p_1/(2j- 1)+\cdots+ p_m/(2j-1)^m)\), where \(p_1,\dots,p_m\) are certain constants. As application, they present the connection between the generalized Wilf and Mortini problems.
Reviewer: József Sándor (Cluj-Napoca)
MSC:
33B15 | Gamma, beta and polygamma functions |
Software:
DLMFOnline Encyclopedia of Integer Sequences:
Decimal expansion of Wilf’s formula: Product_{k>=1} exp(-1/k)*(1 + 1/k + 1/(2*k^2)) = exp(-gamma)*cosh(Pi/2)/(Pi/2).References:
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