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.

In: Computational Methods and Function Theory, Vol. 22, 2022, p. 471–489.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Askitis, D & Pedersen, HL 2022, 'Ratios of Entire Functions and Generalized Stieltjes Functions', Computational Methods and Function Theory, vol. 22, pp. 471–489. https://doi.org/10.1007/s40315-021-00405-5

APA

Askitis, D., & Pedersen, H. L. (2022). Ratios of Entire Functions and Generalized Stieltjes Functions. Computational Methods and Function Theory, 22, 471–489. https://doi.org/10.1007/s40315-021-00405-5

Vancouver

Askitis D, Pedersen HL. Ratios of Entire Functions and Generalized Stieltjes Functions. Computational Methods and Function Theory. 2022;22:471–489. https://doi.org/10.1007/s40315-021-00405-5

Author

Askitis, Dimitris ; Pedersen, Henrik L. / Ratios of Entire Functions and Generalized Stieltjes Functions. In: Computational Methods and Function Theory. 2022 ; Vol. 22. pp. 471–489.

Bibtex

@article{593a6d2f8e024e52b96b51d3c4cbb672,
title = "Ratios of Entire Functions and Generalized Stieltjes Functions",
abstract = "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{\textquoteright}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{\textquoteright}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.",
keywords = "Barnes G-function, Entire function, Euler{\textquoteright}s Gamma function, Generalized Stieltjes function, Laplace transform",
author = "Dimitris Askitis and Pedersen, {Henrik L.}",
note = "Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2022",
doi = "10.1007/s40315-021-00405-5",
language = "English",
volume = "22",
pages = "471–489",
journal = "Computational Methods and Function Theory",
issn = "1617-9447",
publisher = "Springer",

}

RIS

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