A269443 Continued fraction expansion of the Dirichlet eta function at 2.

0, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 3, 2, 2, 4, 1, 1, 1, 1, 1, 1, 4, 1, 6, 3, 7, 1, 7, 3, 3, 2, 4, 2, 2, 1, 1, 2, 1, 1, 3, 2, 1, 5, 1, 3, 1, 2, 1, 1, 13, 40, 1, 1, 1, 48, 211, 4, 91, 1, 16, 9, 1, 10, 8, 2, 4, 1, 2, 3, 2, 1, 1, 13, 3, 1, 2, 2, 1, 3, 1, 18, 2, 1, 1, 1, 5, 3, 7, 1, 1, 21, 1, 6, 4, 1, 1, 2, 1, 3, 2

Offset

0,3

Comments

Continued fraction expansion of Sum_{k>=1} (-1)^(k-1)/k^2 = Zeta(2)/2 = Pi^2/12 = 0.8224670334241132182362...

Links

Table of n, a(n) for n=0..99.

OEIS Wiki, Euler's alternating zeta function

Eric Weisstein's World of Mathematics, Dirichlet Eta Function

Wikipedia, Dirichlet Eta Function

Index entries for continued fractions for constants

Example

1/1^2 - 1/2^2 + 1/3^2 - 1/4^2 + 1/5^2 - 1/6^2 +... = 1/(1 + 1/(4 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + 1/...)))))).

Mathematica

ContinuedFraction[Pi^2/12, 100]

Prog

(PARI) contfrac(Pi^2/12) \\ Michel Marcus, Feb 26 2016

Crossrefs

Cf. A013679, A072691.

Sequence in context: A265143 A181873 A229293 * A039927 A336722 A073802

Adjacent sequences: A269440 A269441 A269442 * A269444 A269445 A269446

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Feb 26 2016

Status

approved