An explicit formula for the generalized Bernoulli polynomials

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.

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 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 Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

Congruences for Generalized q-Bernoulli Polynomials

In this paper, we give some further properties of p-adic q-L-function of two variables, which is recently constructed by Kim 2005 and Cenkci 2006 . One of the applications of these properties yields general classes of congruences for generalized q-Bernoulli polynomials, which are qextensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000 , Gunaratne 1995 , an...