Ratios of Entire Functions and Generalized Stieltjes Functions
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Ratios of Entire Functions and Generalized Stieltjes Functions. / Askitis, Dimitris; Pedersen, Henrik L.
I: Computational Methods and Function Theory, Bind 22, 2022, s. 471–489.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Ratios of Entire Functions and Generalized Stieltjes Functions
AU - Askitis, Dimitris
AU - Pedersen, Henrik L.
N1 - Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022
Y1 - 2022
N2 - Monotonicity properties of the ratio logf(x+a1)⋯f(x+an)f(x+b1)⋯f(x+bn),where f is an entire function are investigated. Earlier results for Euler’s gamma function and other entire functions of genus 1 are generalised to entire functions of genus p with negative zeros. Derivatives of order comparable to p of the expression above are related to generalised Stieltjes functions of order p+ 1. Our results are applied to the Barnes multiple gamma functions. We also show how recent results on the behaviour of Euler’s gamma function on vertical lines can be sharpened and generalised to functions of higher genus. Finally a connection to the so-called Prouhet-Tarry-Escott problem is described.
AB - Monotonicity properties of the ratio logf(x+a1)⋯f(x+an)f(x+b1)⋯f(x+bn),where f is an entire function are investigated. Earlier results for Euler’s gamma function and other entire functions of genus 1 are generalised to entire functions of genus p with negative zeros. Derivatives of order comparable to p of the expression above are related to generalised Stieltjes functions of order p+ 1. Our results are applied to the Barnes multiple gamma functions. We also show how recent results on the behaviour of Euler’s gamma function on vertical lines can be sharpened and generalised to functions of higher genus. Finally a connection to the so-called Prouhet-Tarry-Escott problem is described.
KW - Barnes G-function
KW - Entire function
KW - Euler’s Gamma function
KW - Generalized Stieltjes function
KW - Laplace transform
UR - http://www.scopus.com/inward/record.url?scp=85112360328&partnerID=8YFLogxK
U2 - 10.1007/s40315-021-00405-5
DO - 10.1007/s40315-021-00405-5
M3 - Journal article
AN - SCOPUS:85112360328
VL - 22
SP - 471
EP - 489
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
SN - 1617-9447
ER -
ID: 276855951