Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

3 results

  • IRRATIONALITY OF ZEROS OF POLYGAMMA FUNCTIONS

  • Part of
  • PREETI GOYAT
  • Journal:
    Bulletin of the Australian Mathematical Society , First View
    Published online by Cambridge University Press:
    10 February 2025, pp. 1-11
    • Article
      • You have access
    • PDF
    • HTML
    • Export citation

  • Our work owes its origin to a recent note of Ram Murty [‘Irrationality of zeros of the digamma function’, Number Theory in Memory of Eduard Wirsing (eds. H. Maier, R. Steuding and J. Steuding) (Springer, Cham, 2023), 237–243], in which he proves that all the zeros of the digamma function are irrational with at most one possible exception. We extend this investigation to higher-order polygamma functions.

  • COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE DIVIDED DIFFERENCE OF PSI FUNCTIONS

  • Part of
  • FENG QI, PIETRO CERONE, SEVER S. DRAGOMIR
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 88 / Issue 2 / October 2013
    Published online by Cambridge University Press:
    18 January 2013, pp. 309-319
    Print publication:
    October 2013
    • Article
      • You have access
    • PDF
    • Export citation

  • Necessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions, and the ratio of two gamma functions.

  • A completely monotonic function involving the divided difference of the psi function and an equivalent inequality involving sums

  • Feng Qi
  • Journal:
    The ANZIAM Journal / Volume 48 / Issue 4 / April 2007
    Published online by Cambridge University Press:
    17 February 2009, pp. 523-532
    • Article
      • You have access
    • PDF
    • Export citation

  • In this paper, a function involving the divided difference of the psi function is proved to be completely monotonic, a class of inequalities involving sums is found, and an equivalent relation between complete monotonicity and one of the class of inequalities is established.