A321161 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).
8, 9, 6, 8, 7, 1, 2, 4, 2, 1, 6, 7, 3, 7, 9, 0, 2, 1, 6, 9, 0, 2, 3, 0, 3, 1, 9, 0, 8, 6, 3, 6, 7, 0, 0, 5, 6, 2, 2, 5, 3, 0, 6, 4, 9, 0, 8, 1, 7, 0, 4, 8, 8, 6, 6, 8, 1, 5, 7, 7, 9, 0, 1, 6, 5, 1, 9, 6, 6, 4, 5, 2, 8, 0, 3, 9, 1, 5, 6, 8, 8, 1, 8, 6, 7, 3, 0
Offset: 0
Examples
0.896871242167379021690230319086367005622530649081704...
References
- H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2011, p. 366.
Links
- Chao-Ping Chen and Richard B. Paris, Generalizations of two infinite product formulas, Integral Transforms and Special Functions, Vol. 25, No. 7 (2014), pp. 547-551.
- Chao-Ping Chen and Richard B. Paris, On the asymptotics of products related to generalizations of the Wilf and Mortini problems, Integral Transforms and Special Functions, Vol. 27, No. 4 (2016), pp. 281-288, alternative link.
- Chao-Ping Chen and Richard B. Paris, On the asymptotic expansions of products related to the Wallis, Weierstrass, and Wilf formulas, Applied Mathematics and Computation, Vol. 293 (2017), pp. 30-39, preprint, arXiv:1511.09217 [math.CA], 2015.
- Junesang Choi, Jungseob Lee and H.M. Srivastava, A generalization of Wilf's formula, Kodai Mathematical Journal, Vol. 26, No. 1 (2003), pp. 44-48.
- Junesang Choi and H.M. Srivastava, Integral Representations for the Euler-Mascheroni Constant gamma, Integral Transforms and Special Functions, Vol. 21, No. 9 (2010), pp. 675-690.
- J. Lopez-Bonilla and R. López-Vázquez, On an Identity of Wilf for the Euler-Mascheroni's Constant, Prespacetime Journal, Vol. 9, No. 6 (2018), pp. 516-518.
- Herbert S. Wilf, Problem 10588, The American Mathematical Monthly, Vol. 104, No. 5 (1997), p. 456.
Programs
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Mathematica
RealDigits[Exp[-EulerGamma]*Cosh[Pi/2]/(Pi/2), 10, 100][[1]]
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PARI
exp(-Euler)*cosh(Pi/2)/(Pi/2) \\ Michel Marcus, Jan 15 2019
Comments