Displaying similar documents to “The Θ -transformation of certain positive linear operators.”

On a class of Szász-Mirakyan type operators

Zbigniew Walczak (2008)

Czechoslovak Mathematical Journal

Similarity:

The actual construction of the Szász-Mirakyan operators and its various modifications require estimations of infinite series which in a certain sense restrict their usefulness from the computational point of view. Thus the question arises whether the Szász-Mirakyan operators and their generalizations cannot be replaced by a finite sum. In connection with this question we propose a new family of linear positive operators.

Rational values of the arccosine function

Juan Varona (2006)

Open Mathematics

Similarity:

We give a short proof to characterize the cases when arccos(√r), the arccosine of the squareroot of a rational number r ∈ [0, 1], is a rational multiple of π: This happens exactly if r is an integer multiple of 1/4. The proof relies on the well-known recurrence relation for the Chebyshev polynomials of the first kind.