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

0,1

Comments

The formula was discovered by Wilf in 1997.

References

H. M. Srivastava and Junesang Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier, 2011, p. 366.

Links

Table of n, a(n) for n=0..86.

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.

Example

0.896871242167379021690230319086367005622530649081704...

Mathematica

RealDigits[Exp[-EulerGamma]*Cosh[Pi/2]/(Pi/2), 10, 100][[1]]

Prog

(PARI) exp(-Euler)*cosh(Pi/2)/(Pi/2) \\ Michel Marcus, Jan 15 2019

Crossrefs

Cf. A001620, A042972, A049006, A073004, A080130.

Sequence in context: A203146 A203128 A178856 * A172081 A154842 A195057

Adjacent sequences: A321158 A321159 A321160 * A321162 A321163 A321164

Keyword

nonn,cons

Author

Amiram Eldar, Jan 11 2019

Status

approved