Meixner polynomials and nonvanishing holomorphic functions
نویسندگان
چکیده
منابع مشابه
Meixner Functions and Polynomials Related to Lie Algebra Representations
The decomposition of the tensor product of a positive and a negative discrete series representation of the Lie algebra su(1, 1) is a direct integral over the principal unitary series representations. In the decomposition discrete terms can occur, and the discrete terms are a finite number of discrete series representations or one complementary series representation. The interpretation of Meixne...
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The paper deals with a 3-parameter family of probability measures on the set of partitions, called the z-measures. The z-measures first emerged in connection with the problem of harmonic analysis on the infinite symmetric group. They are a special and distinguished case of Okounkov’s Schur measures. It is known that any Schur measure determines a determinantal point process on the 1-dimensional...
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...
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The class S of functions g(z) = z + c 2 z 2 + c 3 z 3 + ... analytic and univalent in the unit disk Izr < 1 has been thoroughly studied, and its properties are well known. Our purpose is to investigate another class of functions which, by contrast, seems to have been rather neglected. This is the class S o of functions f ( z ) = 1 + a 1 z + a 2 z Z + . . , analytic, univalent, and nonvanishing ...
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
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2001
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(00)00664-6