A269482 Continued fraction expansion of the Dirichlet eta function at 5.

0, 1, 34, 1, 6, 1, 1, 3, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 35, 3, 1, 5, 4, 1, 2, 2, 1, 4, 1, 1, 1, 2, 10, 2, 1, 6, 9, 23, 1, 5, 1, 1, 1, 1, 1, 2, 1, 3, 4, 1, 2, 1, 1, 2, 2, 1, 1, 5, 4, 7, 1, 1, 1, 1, 2, 2, 1, 4, 1, 1, 2, 8, 3, 2, 1, 3, 1, 5, 356, 2, 57, 6, 1, 6, 1, 1, 31, 1, 5, 1, 1, 477, 1, 9, 7, 3, 4

Offset: 0

Author

Ilya Gutkovskiy, Feb 27 2016

Keywords

• nonn
• cofr

Comments

Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^5 = (15*zeta(5))/16 = 0.9721197704469093...

Examples

			1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 +... = 1/(1 + 1/(34 + 1/(1 + 1/(6 + 1/(1 + 1/(1 + 1/...)))))).
		

Links

• 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

Crossrefs

Cf. A013681, A267316.

Programs

Mathematica

ContinuedFraction[(15 Zeta[5])/16, 100]