On a symmetry in strong distributions

摘要

A strong Stieltjes distribution dψ(t) is called symmetric if it satisfies the propertytωdψ(β2/t)=−(β2/t)ωdψ(t),fort∈(a,b)⊆(0,∞),2ω∈Z,andβ>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.