On a symmetry in strong distributions

A strong Stieltjes distribution dψ(t) is called symmetric if it satisfies the propertytω dψ(β2/t)=−(β2/t)ω dψ(t), for t∈(a,b)⊆(0,∞),2ω∈Z, and β>0.In this article some consequences of symmetry on the moments, the orthogonal L-polynomials and the quadrature formulae associated with the distribution are given.