In this paper, we introduce the notion of complete joint Jacobi polynomial two linear codes length n over $${\mathbb {F}}_{q}$$ and {Z}}_{k}$$ . We give MacWilliams type identity for polynomials codes. also concepts average a representation in terms compositions its distribution Further present generalization $$(g+1)$$ -fold Finally, intersection number

The fourth, missing example of an exactly solvable complex potential with PT symmetry V (x) = [V (−x)] * defined on a bent contour and leading, at the real energies, to the Jacobi polynomial wave functions is found in a generalized Hulthén interaction.

We develop a new technique for deriving asymptotic series expansions for moments of combinatorial generating functions that uses the transformation theory of Jacobi forms and “mock” Jacobi forms, as well as the Hardy-Ramanujan Circle Method. The approach builds on a suggestion of Zagier, who observed that the moments of a combinatorial statistic can be simultaneously encoded as the Taylor coeff...

The first part of the paper is devoted to two descriptions all polynomial tau-functions KP hierarchy: by a generalized Jacobi-Trudy formula, and Giambelli formula. We use latter formula in second obtain CKP hierarchy its n-reductions. In particular, for n=3 we find Kaup-Kupershmidt hierarchy.

A holomorphic representation of the Jacobi algebra hn⋊sp(n,R) by first order differential operators with polynomial coefficients on the manifold C × Dn is presented. The Hilbert space of holomorphic functions on which the holomorphic first order differential operators with polynomials coefficients act is constructed.

A collocation-//"'-Galerkin method is defined for some elliptic boundary value problems on a rectangle. The method uses tensor products of discontinuous piecewise polynomial spaces and collocation based on Jacobi points with weight function >c2(l x)2. Optimal order of L2 rates of convergence is established for the approximation solution. A numerical example which confirms these results is prese...

In a recent paper by the authors, a bounded version of Göllnitz's (big) partition theorem was established. Here we show among other things how this theorem leads to nontrivial new polynomial analogues of certain fundamental identities of Jacobi and Lebesgue. We also derive a two parameter extension of Jacobi's famous triple product identity.