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A092042 Decimal expansion of e^(1/4).

%I A092042 #43 Jun 04 2025 00:28:56
%S A092042 1,2,8,4,0,2,5,4,1,6,6,8,7,7,4,1,4,8,4,0,7,3,4,2,0,5,6,8,0,6,2,4,3,6,
%T A092042 4,5,8,3,3,6,2,8,0,8,6,5,2,8,1,4,6,3,0,8,9,2,1,7,5,0,7,2,9,6,8,7,2,2,
%U A092042 0,7,7,6,5,8,6,7,2,3,8,0,0,2,7,5,3,3,0,6,4,1,9,4,3,9,5,5,3,5,6,8
%N A092042 Decimal expansion of e^(1/4).
%C A092042 e^(1/4) is also the integral from 0 to infinity of  e^(-x) * I_0(sqrt(x)), where I_0(z) is a modified Bessel function. - _Jean-François Alcover_, Mar 10 2011
%C A092042 e^(1/4) maximizes the value of x^(c/(x^4)) for any real positive constant c, and minimizes for it for a negative constant, on the range x > 0. - _A.H.M. Smeets_, Aug 16 2018
%H A092042 Vincenzo Librandi, <a href="/A092042/b092042.txt">Table of n, a(n) for n = 1..10000</a>
%H A092042 D. M. Bătinetu-Giurgiu, <a href="https://cms.math.ca/publications/crux/issue?volume=42&amp;issue=4">Problem 4133</a>, Crux Mathematicorum, Vol. 42, No. 4 (2016), p. 174; <a href="https://cms.math.ca/publications/crux/issue?volume=43&amp;issue=4">Solution to Problem 4133</a>, ibid., Vol. 43, No. 4 (2017), pp. 167-169.
%H A092042 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A092042 e^(1/4) = 1/2*( 1 +(5 +(9 +(13 +...)/12)/8)/4 ) = 1 +(1 +(1 +(1 +...)/12)/8)/4. - _Rok Cestnik_, Jan 19 2017
%F A092042 Equals lim_{n->oo} ((2*n-1)!!)^(1/(2*n))/A057863(n)^(1/n^2) (Bătinetu-Giurgiu, 2016). - _Amiram Eldar_, Apr 10 2022
%F A092042 Equals (Integral_{x=1..oo} 1/(x*log(x)^log(log(x))) dx)/sqrt(Pi). - _Kritsada Moomuang_, Jun 03 2025
%e A092042 1.28402541668774148407342056806243645833....
%p A092042 evalf(exp(1/4)); # _Muniru A Asiru_, Aug 16 2018
%t A092042 RealDigits[(E)^(1/4), 10, 100][[1]] (* _Vincenzo Librandi_, Mar 01 2013 *)
%o A092042 (PARI) exp(1/4) \\ _Michel Marcus_, Jan 19 2017
%Y A092042 Cf. A001113, A019774, A057863, A078688, A092426.
%K A092042 cons,nonn
%O A092042 1,2
%A A092042 _Mohammad K. Azarian_, Mar 27 2004