|
%I #19 Jun 16 2022 03:19:35
%S 23,7,9,3,1,1,591,2,9,1,2,34,1,16,1,30,1,1,4,1,2,108,2,2,1,3,1,7,1,2,
%T 2,2,1,2,3,2,166,1,2,1,4,8,10,1,1,7,1,2,3,566,1,2,3,3,1,20,1,2,19,1,3,
%U 2,1,2,13,2,2,11,3,1,2,1,7,2,1,1,1,2,1,19,1,1,12,11,1,4,1,6,1,2,18,1,2
%N Continued fraction for e^Pi.
%C "The transcendentality of e^{Pi} was proved in 1929." (Wells)
%D Jan Gullberg, "Mathematics, From the Birth of Numbers," W. W. Norton and Company, NY and London, 1997, page 86.
%D David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 81.
%H Harry J. Smith, <a href="/A058287/b058287.txt">Table of n, a(n) for n = 0..20000</a>
%H V. Yu. Irkhin, <a href="https://arxiv.org/abs/2206.07174">Relations between e and Pi: Nilakantha's series and Stirling's formula</a>, arXiv:2206.07174 [math.HO], 2022.
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e e^Pi = 23.140692632779269005... = 23 + 1/(7 + 1/(9 + 1/(3 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 19 2009
%p with(numtheory): cfrac(evalf((exp(1))^(evalf(Pi)),2560),256,'quotients');
%t ContinuedFraction[ E^Pi, 100]
%o (PARI) \p 300 contfrac(exp(1)^Pi)
%o (PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(exp(1)^Pi); for (n=0, 20000, write("b058287.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Apr 19 2009
%Y Cf. A039661.
%K cofr,nonn,easy
%O 0,1
%A _Robert G. Wilson v_, Dec 07 2000
%E More terms from _Jason Earls_, Jun 21 2001
|
