Inequalities Involving Gamma and Psi Functions
Document Type
Article
Publication Date
2003
Keywords
Gamma function, digamma function, inequalities, complete monotonicity
Digital Object Identifier (DOI)
https://doi.org/10.1142/S0219530503000041
Abstract
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.
Was this content written or created while at USF?
Yes
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.
https://digitalcommons.usf.edu/mth_facpub/126
