In a previous paper [Proc. Am. Math. Soc. 131, No. 11, 3335–3344 (2003; Zbl 1113.11040)] the author, inspired by the work of Beukers on the irrationality of and , considered the following sequence of double integrals
and proved that . He then used this property to derive interesting criteria for the irrationality of Euler’s constant .
In this paper he continues these investigations and obtains the equivalent single integral
by first showing that this single integral is equal to a Nesterenko-type series, which when replaced in the expression one obtains the same linear combination. In an appendix, S. Zlobin proves again, but without expanding in linear forms, that the double integral equals that Nesterenko-type series. Sondow hopes that the variety of expressions for will turn out to be useful in determining the arithmetic nature of .