Some new identities for ζ(k)

Experimental Determination of Apéry-like Identities for ς(2n + 2)

“…We compare (13) to a result due to Leshchiner [17] which is stated incorrectly in [1], and which, as the authors say, has a different flavor: for complex x not an integer,…”

Some rapidly converging series for $\zeta (2n+1)$

“…359]), Koshliakov [18], Leshchiner [19], Grosswald ([14] and [15]), Terras [25], Cohen [7], Butzer et al ([5] and [6]), Dabrowski [9], and others (see, e.g., Berndt [4, pp. 275 and 276]).…”

Congruences arising from Apéry-type series for zeta values

“…Recently, R. Tauraso [13] showed that Apéry's famous series for ζ(3) and ζ(2), k , that were used in his irrationality proofs [9] of these numbers admit very nice panalogues: where a ∈ C, |a| < 1, was given by Koecher [6] (and independently in an expanded form by Leshchiner [7]). Expanding the right-hand side of (4) in powers of a 2 and comparing coefficients of a 2n on both sides of (4) gives the Apéry-like series for ζ(2n+3).…”

“…First results related to generating function identities for even zeta values belong to Leshchiner [7] who proved (in an expanded form) that for |a| < 1,…”