Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences We study the possible growth of Pólya frequency sequence generating functions analytic in the unit disk and describe the proximate orders of growth of these functions. Some classical function theory results concerning orders of growth are generalized to the case of proximate orders. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

On the Proximate Order of Growth of Generating Functions of Pólya Frequency Sequences

Download PDF
23 pages

Loading next page...
 
/lp/springer-journals/on-the-proximate-order-of-growth-of-generating-functions-of-p-lya-2gL6HadEBx
Publisher
Springer Journals
Copyright
Copyright © 2001 by Heldermann Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321001
Publisher site
See Article on Publisher Site

Abstract

We study the possible growth of Pólya frequency sequence generating functions analytic in the unit disk and describe the proximate orders of growth of these functions. Some classical function theory results concerning orders of growth are generalized to the case of proximate orders.

Journal

Computational Methods and Function Theory – Springer Journals

Published: Mar 7, 2013

References

  • On the generating functions of totally positive sequences
    Aissen, M; Edrei, A; Schoenberg, I J; Whitney, A
  • Wachtumsordnung, Koeffizientenwachstum und Nullstellendichte bei Potenzreihen mit endlichem Konvergenzkreis
    Beuermann, F
  • Analytische Fortsetzung
    Bieberbach, L
  • Beitrag zur Theorie der ganzen Funktionen
    Faber, G
  • Sur un théorème de MM. Wigert-Leau
    Gelfond, A O
  • Total Positivity
    Karlin, S
  • Zero sets of entire generating functions of Pólya frequency sequences of finite order
    Katkova, O M; Ostrovskii, I V
  • Transl. Math. Monographs, vol. 5
    Levin, B Ya.
  • Associated integral functions and singular points of power series
    Macintyre, A J; Wilson, R
  • On the zeros of the generating functions of Multiply positive sequences and functions
    Schoenberg, I J
  • Regularly Varying Functions
    Seneta, E
  • On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion
    Seremeta, M N
  • O svyazi mezhdu rostom tselykh ili analiticheskikh v krugie funktsiy nulevovo poryadka i koeffitsientami ikh stepennyh razlozheniy
    Sheremeta, M N