منابع مشابه
More zeros of krawtchouk polynomials
Three theorems are given for the integral zeros of Krawtchouk polynomials. First, five new infinite families of integral zeros for the binary (q = 2) Krawtchouk polynomials are found. Next, a lower bound is given for the next integral zero for the degree four polynomial. Finally, three new infinite families in q are found for the degree three polynomials. The techniques used are from elementary...
متن کاملZeros of Generalized Krawtchouk Polynomials
The zeros of generalized Krawtchouk polynomials are studied. Some interlacing theorems for the zeros are given. A new infinite family of integral zeros is given, and it is conjectured that these comprise most of the non-trivial zeros. The integral zeros for two families of q-Krawtchouk polynomials are classified.
متن کاملReal zeros of Meixner and Krawtchouk polynomials
We use a generalised Sturmian sequence argument and the discrete orthogonality of the Krawtchouk polynomials for certain parameter values to prove that all the zeros of Meixner polynomials are real and positive for parameter ranges where they are no longer orthogonal. AMS MOS Classification: 33C45, 34C10, 42C05
متن کاملZeros of Meixner and Krawtchouk polynomials
We investigate the zeros of a family of hypergeometric polynomials 2F1(−n,−x; a; t), n ∈ N that are known as the Meixner polynomials for certain values of the parameters a and t. When a = −N, N ∈ N and t = p , the polynomials Kn(x; p,N) = (−N)n2F1(−n,−x;−N; p ), n = 0, 1, . . .N, 0 < p < 1 are referred to as Krawtchouk polynomials. We prove results for the zero location of the orthogonal polyno...
متن کاملOn Integral Zeros of Krawtchouk Polynomials
We derive new conditions for nonexistence of integral zeros of binary Krawtchouk polynomials. Upper bounds for the number of integral roots of Krawtchouk polynomials are presented.
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ژورنال
عنوان ژورنال: Graphs and Combinatorics
سال: 1993
ISSN: 0911-0119,1435-5914
DOI: 10.1007/bf02988302