On irrationality measures of

We prove that the number , where d∈Z, |d|>1, and r,s∈Q, s≠0, are such that 1+djr+d2js≠0 for any j∈Z+, has an irrationality measure 7/3 or 7/2 depending on whether r=−d−h−sdh for some h∈N or r2⩽4s. More generally, irrationality measures are given for τ in both the archimedean and p-adic valuations, and also when d,r,s are certain algebraic numbers. For example, we give an effective irrationality measure 7/3 for Bd(d), where Bq(z) is a q-analogue of the Bessel function, and we get effective irrationality measures 7/3 and 7/2 for the p-adic numbers and , respectively, where .