A086056 Decimal expansion of Pi/(2e).
5, 7, 7, 8, 6, 3, 6, 7, 4, 8, 9, 5, 4, 6, 0, 8, 5, 8, 9, 5, 5, 0, 4, 6, 5, 9, 1, 6, 5, 6, 3, 4, 8, 1, 4, 9, 5, 6, 0, 4, 2, 5, 5, 1, 1, 5, 8, 2, 2, 0, 7, 9, 1, 0, 2, 4, 9, 8, 5, 3, 2, 6, 7, 6, 6, 3, 6, 4, 4, 3, 1, 5, 9, 2, 0, 4, 5, 8, 4, 6, 9, 7, 2, 0, 0, 9, 4, 2, 1, 7, 1, 1, 7, 8, 3, 6, 7, 7, 9, 4, 0, 2
Offset: 0
Examples
0.57786367489546085895504659165634814956042551...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Sections 1.4.3 and 7.2, pp. 22, 459.
Links
- Victor S. Adamchik, The Multiple Gamma Function and Its Application to Computation of Series, Ramanujan J. vol. 9, no 3. (2005) 271-288.
- Christophe Chesneau, An original approximation involving Pi, the Euler-Mascheroni constant and the Catalan constant, hal-04692308, [math], 2024.
- Christophe Chesneau, On Surprising Approximations Involving Multiple Mathematical Constants, Pan-Amer. J. Math. (2025) Vol. 4, No. 2. See p. 8.
- Zdzislaw A. Melzak, Infinite products for πe and π/e, Amer. Math. Monthly 68 (1961) 39-41.
- Eric Weisstein's World of Mathematics, Euler-Mascheroni Constant Approximations.
- Eric Weisstein's World of Mathematics, InfiniteProduct.
- Eric Weisstein's World of Mathematics, Masser-Gramain Constant.
Crossrefs
Cf. A216184 (Integral_{x>=0} sin(x)/(x^2+1)).
Programs
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Maple
Digits:=100: evalf(Pi/(2*exp(1))); # Wesley Ivan Hurt, Jan 07 2017
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Mathematica
First@ RealDigits@ N[Pi/(2 E), 120] (* Michael De Vlieger, Jan 07 2017 *)
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PARI
Pi/(2*exp(1)) \\ Michel Marcus, Jan 07 2017
Formula
Equals Integral_{x>=0} cos(x)/(x^2+1) dx = Integral_{x>=0} x*sin(x)/(x^2+1) dx. - Jean-François Alcover, Mar 28 2013
Equals Product_{k>=1} (1 + 2/k)^((-1)^(k+1) * k). - Amiram Eldar, Jul 16 2020