Korobov Polynomials of the Fifth Kind and of the Sixth Kind
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Recently, Korobov polynomials have been received a lot of attention, whichare discrete analogs of Bernoulli polynomials. In particular, these polynomials are used toderive some interpolation formulas of many variables and a discrete analog of the Eulersummation formula. In this paper, we extend these family of polynomials to consider theKorobov polynomials of the fth kind and of the sixth kind. We present several explicitformulas and recurrence relations for these polynomials. Also, we establish a connectionbetween our polynomials and several known families of polynomials.
Abstract
Recently, Korobov polynomials have been received a lot of attention, whichare discrete analogs of Bernoulli polynomials. In particular, these polynomials are used toderive some interpolation formulas of many variables and a discrete analog of the Eulersummation formula. In this paper, we extend these family of polynomials to consider theKorobov polynomials of the fth kind and of the sixth kind. We present several explicitformulas and recurrence relations for these polynomials. Also, we establish a connectionbetween our polynomials and several known families of polynomials.
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