An explicit formula for generalized potential polynomials and its applications

An Explicit Formula for Lanczos Polynomials*

The Lanczos algorithm for tridiagonalizing a given matrix A generates a sequence of approximating matrices A, that can naturally be obtained as restrictions to subspaces. The eigenvalues of these approximating matrices are well known to be good approximations to the extreme eigenvalues of A. In this paper we produce explicit formulas for the characteristic polynomials of the A,, in terms of the...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

An Explicit Formula for the Euler Product of Hecke Polynomials

An explicit formula is given for a sequence of numbers by using the Eichler-Selberg trace formula. A criterion is obtained by using these numbers for the location of nontrivial zeros of Hecke L-functions, which are associated with a family of cusp forms of weight 2.

An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials

Explicit expressions for restricted partition function W (s,d) and its quasiperiodic components Wj(s,d ) (called Sylvester waves) for a set of positive integers d = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli polynomials of higher order with periodic coefficients.

Pieri’s Formula for Generalized Schur Polynomials

Young’s lattice, the lattice of all Young diagrams, has the Robinson-Schensted-Knuth correspondence, the correspondence between certain matrices and pairs of semi-standard Young tableaux with the same shape. Fomin introduced generalized Schur operators to generalize the Robinson-Schensted-Knuth correspondence. In this sense, generalized Schur operators are generalizations of semi-standard Young...