We investigate interlacing properties of zeros Laguerre polynomials Ln(α)(x) and Ln+1(α+k)(x), α>−1, where n∈N k∈{1,2}. prove that, in general, the these interlace partially not fully. The sharp t-interval within which two equal degree Ln(α+t)(x) are for every each α>−1 is 0<t≤ 2, [Driver K, Muldoon ME. Sharp interval polynomials. J Approx Theory, to appear.], consecutive Ln−1(α+t)(x) 0≤t≤ Comm...

the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.

We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original and noise have regularly-varying tails, tail indices α,α′>0, respectively. is taken as Karlin model, recently investigated model that has characterized memory parameter β∈(0,1). establish limit theorems for extremes reveal phase transition. In terms ther...