Inequalities Involving Gamma and Psi Functions
Gamma function, digamma function, inequalities, complete monotonicity
Digital Object Identifier (DOI)
We prove that certain functions involving the gamma and q-gamma function are monotone. We also prove that (xmψ(x))(m+1) is completely monotonic. We conjecture that -(xmψ(m)(x))(m) is completely monotonic for m ≥ 2; and we prove it, with help from Maple, for 2 ≤ m ≤ 16. We give a very useful Maple procedure to verify this for higher values of m. A stronger result is also formulated where we conjecture that the power series coefficients of a certain function are all positive.
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Citation / Publisher Attribution
Analysis and Applications, v. 1, issue 1, p. 129-140
Scholar Commons Citation
Clark, W. Edwin and Ismail, Mourad E. H., "Inequalities Involving Gamma and Psi Functions" (2003). Mathematics and Statistics Faculty Publications. 126.