In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families linear bilinear generating functions which are associated with orthogonal polynomials such other higher transcendental as (for example) hypergeometric in one, two more variables. Many the results well methods techniques used for their derivations, presented here, intended ...

Cucurbit[7[uril, the wheel component in two new and structurally simple pseudorotaxanes, shuttles between the two axle termini at low pH, whereas the shuttling motion stops at higher pH, as the wheel is bound to the center of the axle.

In this paper, we construct four infinite families of ternary linear codes associated with double cosets in O(2n+1, q) with respect to certain maximal parabolic subgroup of the special orthogonal group SO(2n + 1, q). Here q is a power of three. Then we obtain two infinite families of recursive formulas , the one generating the power moments of Kloosterman sums with " trace nonzero square argume...

The main aim of this paper is to construct a multivariable extension with the help of the extended Jacobi matrix polynomials (EJMPs). Generating matrix functions and recurrence relations satisfied by these multivariable matrix polynomials are derived. Furthermore, general families of multilinear and multilateral generating matrix functions are obtained and their applications are presented.

After proving a theorem about the general formulae for the signature of alternating knot and link families, we distinguished all families of knots obtained from generating alternating knots with at most 10 crossings and alternating links with at most 9 crossings, for which the unknotting (unlinking) number can be confirmed by using the general formulae for signatures.

This paper generalizes a method of generating shift sequences in the interleaved construction proposed by Gong. With the new shift sequences, some new families of p-ary sequences with desired properties can be obtained. A lower bound on the number of new families of binary sequences is also established.

In this short note, we give simple proofs of several results and conjectures formulated by Stolarsky and Tran concerning generating functions of some families of Chebyshev-like polynomials.

We present some families of polynomials related to the moments of weight functions of hypergeometric type. We also consider different types of generating functions, and give several examples.