• 대한수학회지
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• 제58권1호
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• pp.133-147
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• 2021

Our aim in this paper is to derive several new monotonicity properties and functional inequalities of some functions involving the q-gamma, q-digamma and q-polygamma functions. More precisely, some classes of functions involving the q-gamma function are proved to be logarithmically completely monotonic and a class of functions involving the q-digamma function is showed to be completely monotonic. As applications of these, we offer upper and lower bounds for this special functions and new sharp upper and lower bounds for the q-analogue harmonic number harmonic are derived. Moreover, a number of two-sided exponential bounding inequalities are given for the q-digamma function and two-sided exponential bounding inequalities are then obtained for the q-tetragamma function.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.233-242
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• 2013

Certain interesting single (or double) infinite series associated with hypergeometric functions have been expressed in terms of Psi (or Digamma) function ${\psi}(z)$, for example, see Nishimoto and Srivastava [8], Srivastava and Nishimoto [13], Saxena [10], and Chen and Srivastava [5], and so on. In this sequel, with a view to unifying and extending those earlier results, we first establish two relations which some double infinite series involving hypergeometric functions are expressed in a single infinite series involving ${\psi}(z)$. With the help of those series relations we derived, we next present two functional relations which some double infinite series involving $\bar{H}$-functions, which are defined by a generalized Mellin-Barnes type of contour integral, are expressed in a single infinite series involving ${\psi}(z)$. The results obtained here are of general character and only two of their special cases, among numerous ones, are pointed out to reduce to some known results.