Question

completa las multiplicaciones
a) 21 x ( - ) = -126
b) ( ) x(-8) =104
c) (9 x(-14) = -144
d) 15 x ( 7 ) = -192
f) -25 x (__) = - 275


Porfabor ayuda :( es para en unos minutos ​

Answer 1

Respuesta:

Let P,(x), n ~> 1 be the orthogonal polynomials defined by

anPn+l(X) -~ an_lPn_l(x) + b.P,(x) = xP,(x), Po(x) = 0, Pl(x) = 1,

where both sequences a, and b, are bounded and a. > 0.

Assume that ~,(x) is the unique (up to a constant) distribution function which corresponds to the measure of

orthogonality of P,(x) and denote by S(~,) the spectrum of ~p(x). Alternative proofs of a theorem due to Stieltjes and of

a conjecture due to Maki concerning the limit points of S(~) are given. A typical example to the Maki's conjecture

together with a general result concerning the density of the zeros of the polynomials P,(x) covers as a particular case

a theorem of Chihara which generalizes the well-known theorem of Blumenthal.

Keywords: Orthogonal polynomials; Measure of orthogonality; Zeros; Limit points of the spectrum

AMS Classification: 42C05

1. Introduction

In [7] Chihara has formulated and proved the following theorem which follows from a result of

Stieltjes [16], concerning continued fractions.

Theorem 1.1 (Stieltjes [16]). Let R. be the set of orthogonal polynomials defined by

a,R,+l(x) + a,-1R,-l(x) = xR,(x), n >~ 1,

(1.1)

Ro(x) = O, RI(x ) = 1.

Then a necessary and sufficient condition for the associated distribution function t~ to have a denumer