Journal of the
Korean Mathematical Society JKMS

Let $\{ K_{\vec n}^{(\vec p; N)}(x) \} $ be a multiple Kravchuk polynomial with respect to $r$ discrete Kravchuk weights. We first find a lowering operator for multiple Kravchuk polynomials $\{ K_{\vec n}^{(\vec p; N)}(x) \} $ in which the orthogonalizing weights are not involved. Combining the lowering operator and the raising operator by Rodrigues' formula, we find a $(r+1)$-th order difference equation which has the multiple Kravchuk polynomials $ \{ K_{\vec n}^{(\vec p; N)}(x) \}$ as solutions. Lastly we give an explicit difference equation for $\{ K_{\vec n}^{(\vec p; N)}(x) \}$ for the case of $r=2$.

Keywords: multiple orthogonal polynomials, Kravchuk polynomials, difference equation, rodrigues' formula

MSC numbers: 33C45, 39A13, 42C05