Root geometry of polynomial sequences I: Type (0,1)
نویسندگان
چکیده
منابع مشابه
Root Geometry of Polynomial Sequences I: Type (0, 1)
This paper is concerned with the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x) = aWn−1(x) + (bx + c)Wn−2(x), with W0(x) = 1 and W1(x) = t(x − r), where a > 0, b > 0, and c, t, r ∈ R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x | Wn(x) = 0...
متن کاملSchur Type Functions Associated with Polynomial Sequences of Binomial Type
We introduce a class of Schur type functions associated with polynomial sequences of binomial type. This can be regarded as a generalization of the ordinary Schur functions and the factorial Schur functions. This generalization satisfies some interesting expansion formulas, in which there is a curious duality. Moreover this class includes examples which are useful to describe the eigenvalues of...
متن کاملGeometry of all supersymmetric type I backgrounds
We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9, 1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in ...
متن کاملComputational Arithmetic Geometry I. Sentences Nearly in the Polynomial Hierarchy
We consider the average-case complexity of some otherwise undecidable or open Diophantine problems. More precisely, consider the following: I. Given a polynomial f ∈Z[v, x, y], decide the sentence ∃v ∀x ∃y f(v, x, y) ? =0, with all three quantifiers ranging over N (or Z). II. Given polynomials f1, . . . , fm∈Z[x1, . . . , xn] with m≥n, decide if there is a rational solution to f1= · · · =fn = 0...
متن کاملPolynomial Sequences of Binomial Type and Path Integrals
Polynomial sequences pn(x) of binomial type are a principal tool in the umbral calculus of enumerative combinatorics. We express pn(x) as a path integral in the “phase space” N× [−π, π]. The Hamiltonian is h(φ) = ∑n=0 p ′ n(0)/n!e inφ and it produces a Schrödinger type equation for pn(x). This establishes a bridge between enumerative combinatorics and quantum field theory. It also provides an a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2016
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2015.08.039