Complete monotonicity of log-functions

2025/05/07 by Rourou Ma, Julian Weigert, Ma, Rourou +1 · 1 citation
Computer Science · Mathematics · #Polynomial and algebraic computation #Mathematical functions and polynomials #Advanced Optimization Algorithms Research

paper · pdf · doi:10.48550/arxiv.2505.04225

Abstract

In this article we investigate the property of complete monotonicity within a special family F_s of functions in s variables involving logarithms. The main result of this work provides a linear isomorphism between F_s and the space of real multivariate polynomials. This isomorphism identifies the cone of completely monotone functions with the cone of non-negative polynomials. We conclude that the cone of completely monotone functions in F_s is semi-algebraic. This gives a finite time algorithm to decide whether a function in F_s is completely monotone

Cited by

• Approximating Feynman Integrals Using Complete Monotonicity and Stieltjes Properties

Related

• Completely and logarithmically completely monotone functions
• Complete Monotonicity of Special Functions
• Logarithmically completely monotontic functions related the q-gamma and the q-digamma functions with applications
• Completely monotonic ratios of basic and ordinary gamma functions
• On a conjecture of a logarithmically completely monotonic function