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A058287 Continued fraction for e^Pi. 5

%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

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)