2020
DOI: 10.48550/arxiv.2007.14924
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Stieltjes moment properties and continued fractions from combinatorial triangles

Abstract: Many famous combinatorial numbers can be placed in the following generalized triangular array [T n,k ] n,k≥0 satisfying the recurrence relation:with T 0,0 = 1 and T n,k = 0 unless 0 ≤ k ≤ n. For n ≥ 0, denote by T n (q) its rowgenerating functions. In this paper, we consider the x-Stieltjes moment property and 3-x-log-convexity of (T n (q)) n≥0 and the linear transformation of T n,k preserving Stieltjes moment properties of sequences.Using total positivity, we develop various criteria for x-Stieltjes moment pr… Show more

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Cited by 2 publications
(6 citation statements)
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“…For example, the Bell polynomials, the classical Eulerian polynomials, the Narayana polynomials of type A and B, Ramanujan polynomials, Dowling polynomials, Jacobi-Stirling polynomials, and so on, are q-log-convex (see Chen et al [20,21], Liu and Wang [58], Zhu [103,104,105,106], Zhu and Sun [113] for instance), 3-q-log-convex (see [107]) and q-Stieltjes moment (see [90,101,107,109]). We refer the reader to [73,74,90,91,110,111,112] for coefficientwise Hankel-total positivity in more indeterminates.…”
Section: Definitions and Notation From Total Positivitymentioning
confidence: 99%
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“…For example, the Bell polynomials, the classical Eulerian polynomials, the Narayana polynomials of type A and B, Ramanujan polynomials, Dowling polynomials, Jacobi-Stirling polynomials, and so on, are q-log-convex (see Chen et al [20,21], Liu and Wang [58], Zhu [103,104,105,106], Zhu and Sun [113] for instance), 3-q-log-convex (see [107]) and q-Stieltjes moment (see [90,101,107,109]). We refer the reader to [73,74,90,91,110,111,112] for coefficientwise Hankel-total positivity in more indeterminates.…”
Section: Definitions and Notation From Total Positivitymentioning
confidence: 99%
“…Proposition 1.12. [110] For a polynomial sequence (A n (x)) n≥0 , if the Hankel matrix [A i+j (x)] i,j≥0 is coefficientwise totally positive of order 4 in x, then (A n (x)) n≥0 is 3-x-logconvex.…”
Section: Rogers Trianglementioning
confidence: 99%
“…Let x = (x i ) i∈I is a set of indeterminates. A polynomial sequence (α n (x)) n≥0 in R[x] is called a x-Stieltjes moment (x-SM for short) sequence if its associated infinite Hankel matrix is x-TP, see Zhu [51,54] for instance. When (α n (x)) n≥0 is a sequence of real numbers, x-SM sequence reduces to the classical Stieltjes moment sequence.…”
Section: Stieltjes Moment Property and Continued Fractionsmentioning
confidence: 99%
“…When (α n (x)) n≥0 is a sequence of real numbers, x-SM sequence reduces to the classical Stieltjes moment sequence. For x-SM sequences, the following criterion was proved in [51,54].…”
Section: Stieltjes Moment Property and Continued Fractionsmentioning
confidence: 99%
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