OFFSET
0,1
COMMENTS
"The transcendentality of e^{Pi} was proved in 1929." (Wells)
REFERENCES
Jan Gullberg, "Mathematics, From the Birth of Numbers," W. W. Norton and Company, NY and London, 1997, page 86.
David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 81.
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..20000
V. Yu. Irkhin, Relations between e and Pi: Nilakantha's series and Stirling's formula, arXiv:2206.07174 [math.HO], 2022.
G. Xiao, Contfrac
EXAMPLE
e^Pi = 23.140692632779269005... = 23 + 1/(7 + 1/(9 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Apr 19 2009
MAPLE
with(numtheory): cfrac(evalf((exp(1))^(evalf(Pi)), 2560), 256, 'quotients');
MATHEMATICA
ContinuedFraction[ E^Pi, 100]
PROG
(PARI) \p 300 contfrac(exp(1)^Pi)
(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
CROSSREFS
KEYWORD
cofr,nonn,easy
AUTHOR
Robert G. Wilson v, Dec 07 2000
EXTENSIONS
More terms from Jason Earls, Jun 21 2001
STATUS
approved