Jeffery Lagarias, in his recent article
*Euler's constant: Euler's work and modern developments*
in the AMS Bulletin, mentions that Euler obtained $\zeta(3)={{2\pi^3 b(3/2)}\over 3}$ for some "Bernoulli function" $b(z)$ in Section 2.4 ("Zeta values") of his article.

Lagarias also mentions that Euler similarly obtained a value for $\zeta(5)$ in terms of $b(5/2)$.

Is there any modern article explaining this "Bernoulli function $b(z)$?