Markov–Sonin Gaussian rule for singular functions

The paper deals with the approximation of integrals ∫Rfwβ, where wβ is a Markov–Sonin weight and f can be singular at the origin. Gaussian-type quadrature rules, having a better behaviour w.r.t. the ordinary Gaussian rule, are introduced. Error estimates in weighted L1 norm and some numerical tests are given.