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2 results

  • 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
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  • 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
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  • 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.