Complete Monotonicity of Special Functions

2015/06/16 by R. Zhang, Zhang, Ruiming
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM) #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1506.07012

openalex publication_date 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we prove that if an entire function f(z) is of order strictly less than one and it has only negative zeros, then for each nonnegative integer k,m the real function (-(1)/(x))^m\fracd^kdx^k(x^k+m\fracd^mdx^m((f'(x))/(f(x)))) is completely monotonic on (0,∞). Applications to Askey-Wilson polynomials, Bessel functions, Ramanujan's entire function, Riemann-xi function and character Riemann-xi functions are also provided.

Related

• On Certain Genus 0 Entire Functions
• On completely monotonic functions
• Conjecture concerning a completely monotonic function
• Zeros of Ramanujan Type Entire Functions
• Several completely monotone functions related to DeTemple's sequence