Criteria for irrationality of generalized Eulerʹs constant

We generalize Sondowʹs (ir)rationality criteria for Eulerʹs constant and give necessary and sufficient conditions for irrationality of generalized Eulerʹs constant γα, as well as obtain new asymptotic formulas for computing γα. The proof is based on constructing linear forms in 1,γα and logarithms of rational numbers.