Complete Monotonicity and Zeros of Sums of Squared Baskakov Functions

TL;DR

This paper investigates the complete monotonicity of sums of squared Baskakov basis functions, analyzes the distribution of zeros for large parameters, and extends results to higher powers, connecting hypergeometric functions and complex analysis.

Contribution

It establishes the complete monotonicity of sums of squared Baskakov functions and explores zero distributions, extending prior work to higher powers and hypergeometric functions.

Findings

Proves complete monotonicity of sums of squared Baskakov functions.

Analyzes zero distribution for large parameters in the Baskakov case.

Extends results to sums of higher powers.

Abstract

We prove complete monotonicity of sums of squares of generalized Baskakov basis functions by deriving the corresponding results for hypergeometric functions. Moreover, in the central Baskakov case we study the distribution of the complex zeros for large values of a parameter. We finally discuss the extension of some results for sums of higher powers.