scholarly journals On the Real-Rootedness of the Descent Polynomials of $(n-2)$-Stack Sortable Permutations

10.37236/4613 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Philip B. Zhang
Keyword(s):  
General Result ◽  
The Real ◽  
Real Zeros ◽  
Eulerian Polynomials

Bóna conjectured that the descent polynomials on $(n-2)$-stack sortable permutations have only real zeros. Brändén proved this conjecture by establishing a more general result. In this paper, we give another proof of Brändén's result by using the theory of $s$-Eulerian polynomials recently developed by Savage and Visontai.

scholarly journals $q$-Eulerian Polynomials and Polynomials with Only Real Zeros

10.37236/741 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
Shi-Mei Ma ◽  
Yi Wang
Keyword(s):  
The Real ◽  
Real Zeros ◽  
Eulerian Polynomials

Let $f$ and $F$ be two polynomials satisfying $F(x)=u(x)f(x)+v(x)f'(x)$. We characterize the relation between the location and multiplicity of the real zeros of $f$ and $F$, which generalizes and unifies many known results, including the results of Brenti and Brändén about the $q$-Eulerian polynomials.

scholarly journals On a partial theta function and its spectrum

2016 ◽  
Vol 146 (3) ◽  
pp. 609-623 ◽  
Author(s):  
Vladimir Petrov Kostov
Keyword(s):  
Entire Function ◽  
Theta Function ◽  
Local Minimum ◽  
Real Zero ◽  
Positive Real ◽  
The Real ◽  
Real Zeros ◽  
Partial Theta Function

The bivariate series defines a partial theta function. For fixed q (∣q∣ < 1), θ(q, ·) is an entire function. For q ∈ (–1, 0) the function θ(q, ·) has infinitely many negative and infinitely many positive real zeros. There exists a sequence of values of q tending to –1+ such that has a double real zero (the rest of its real zeros being simple). For k odd (respectively, k even) has a local minimum (respectively, maximum) at , and is the rightmost of the real negative zeros of (respectively, for k sufficiently large is the second from the left of the real negative zeros of ). For k sufficiently large one has . One has and .

On the real zeros of the function ζ(1/2 +it)

1985 ◽  
Vol 40 (4) ◽  
pp. 191-192
Author(s):  
A A Karatsuba
Keyword(s):  
The Real ◽  
Real Zeros

The Real Zeros of Struve’s Function

1970 ◽  
Vol 1 (3) ◽  
pp. 365-375 ◽  
Author(s):  
J. Steinig
Keyword(s):  
The Real ◽  
Real Zeros

The real zeros of the confluent hypergeometric function

1956 ◽  
Vol 52 (4) ◽  
pp. 626-635 ◽  
Author(s):  
L. J. Slater
Keyword(s):  
Hypergeometric Function ◽  
Numerical Evaluation ◽  
Confluent Hypergeometric Function ◽  
The Real ◽  
Real Zeros ◽  
Image Position

This paper contains a discussion of various points which arise in the numerical evaluation of the small real zeros of the confluent hypergeometric functionwhereThere are two distinct problems, first the determination of those values of x for which M(a, b; x) = 0, given a and b, and secondly the study of the curves represented by M (a, b; x) = 0, for fixed values of x. These curves all lie on the surface M(a, b; x) = 0, of course.

On the real zeros of trigonometrical polynomials

1973 ◽  
Vol 26 (1) ◽  
pp. 235-242
Author(s):  
Zalman Rubinstein
Keyword(s):  
The Real ◽  
Real Zeros
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