Ratios of Entire Functions and Generalized Stieltjes Functions
نویسندگان
چکیده
Monotonicity properties of the ratio $$\begin{aligned} \log \frac{f(x+a_1)\cdots f(x+a_n)}{f(x+b_1)\cdots f(x+b_n)}, \end{aligned}$$where f is an entire function are investigated. Earlier results for Euler’s gamma and other functions genus 1 generalised to p with negative zeros. Derivatives order comparable expression above related Stieltjes \(p+1\). Our applied Barnes multiple functions. We also show how recent on behaviour vertical lines can be sharpened higher genus. Finally a connection so-called Prouhet-Tarry-Escott problem described.
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ژورنال
عنوان ژورنال: Computational Methods and Function Theory
سال: 2021
ISSN: ['2195-3724', '1617-9447']
DOI: https://doi.org/10.1007/s40315-021-00405-5