On Positivity of Linear Combinations of Polynomials

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

On Linear Combinations of Chebyshev Polynomials

a0Tn(x) + a1Tn−1(x) + · · ·+ amTn−m(x) where (a0, a1, . . . , am) is a fixed m-tuple of real numbers, a0, am 6= 0, Ti(x) are Chebyshev polynomials of the first kind, n = m, m + 1, m + 2, . . . Here we analyze the structure of the set of zeros of such polynomial, depending on A and its limit points when n tends to infinity. Also the expression of envelope of the polynomial is given. An applicati...

On Linear Combinations of Orthogonal Polynomials

In this expository paper, linear combinations of orthogonal polynomials are considered. Properties like orthogonality and interlacing of zeros are presented.

Stability of Roots of Polynomials under Linear Combinations of Derivatives

Let T = α0I + α1D + · · · + αnD n , where D is the differentiation operator and α0 = 0, and let f be a square-free polynomial with large minimum root separation. We prove that the roots of T f are close to the roots of f translated by −α1/α0.

Positivity Of Trigonometri Polynomials