A058287 Continued fraction for e^Pi.

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, 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, 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

Offset: 0

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• cofr
• nonn
• easy

Comments

"The transcendentality of e^{Pi} was proved in 1929." (Wells)

Examples

			e^Pi = 23.140692632779269005... = 23 + 1/(7 + 1/(9 + 1/(3 + 1/(1 + ...)))). - _Harry J. Smith_, Apr 19 2009
		

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
• Index entries for continued fractions for constants

Crossrefs

Cf. A039661.

Programs

Maple

with(numtheory): cfrac(evalf((exp(1))^(evalf(Pi)),2560),256,'quotients');

Mathematica

ContinuedFraction[ E^Pi, 100]

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

Extensions

More terms from Jason Earls, Jun 21 2001