A269481 Continued fraction expansion of the Dirichlet eta function at 4.

0, 1, 17, 1, 7, 3, 3, 1, 7, 3, 6, 1, 1, 7, 1, 11, 1, 11, 5, 1, 2, 2, 2, 7, 1, 14, 6, 5, 1, 1, 1, 1, 10, 9, 1, 1, 5, 2, 2, 3, 2, 5, 2, 4, 1, 46, 312, 3, 3, 1, 15, 1, 2, 5, 2, 1, 1, 27, 1, 2, 1, 2, 11, 5, 2, 1, 482, 3, 2, 4, 2, 2, 3, 1, 3, 1, 2, 1, 1, 13, 1, 13, 1, 1, 67, 149, 7, 2, 2, 18, 1, 2, 1, 1, 1, 51, 1, 7, 1, 8

Offset

0,3

Comments

Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^4 = (7*Pi^4)/720 = 0.9470328294972459175765...

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

1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 +... = 1/(1 + 1/(17 + 1/(1 + 1/(7 + 1/(3 + 1/(3 + 1/...)))))).

Mathematica

ContinuedFraction[(7 Pi^4)/720, 100]

Crossrefs

Cf. A013680, A267315.

Sequence in context: A040301 A175960 A040302 * A229201 A040303 A040304

Adjacent sequences: A269478 A269479 A269480 * A269482 A269483 A269484

Keyword

nonn,cofr

Author

Ilya Gutkovskiy, Feb 27 2016

Status

approved