Large and sparse rational eigenproblems where the rational term is of low rank k arise in vibrations of fluid–solid structures and of plates with elastically attached loads. Exploiting model order reduction techniques, namely the Padé approximation via block Lanczos method, problems of this type can be reduced to k–dimensional rational eigenproblems which can be solved efficiently by safeguarde...

We construct approximate formulas for the O(α3 s ) QCD contributions to the vector current correlator, which is valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Padé approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.

Based on the Padé approximation method, we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new bounds for the gamma function.

Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] ([Formula: see text]) such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish new upper bounds for [Formula: see text]. As an application, we give a generalized Carleman-type inequality.