On a conjecture of Clark and Ismail
In this paper the authors prove that there exists an integer \(m_0\) such that for all \(m\geq m_0\) the function \(\phi^{(m)}_m\) is not completely monotonic where \(\phi_m(x)=-x^m\psi^{(m)}(x)\) and \(\psi\) denotes the logarithmic derivative of Euler's gamma function. The findings of this paper disprove a conjecture of \textit{W. E. Clark} and \textit{M. E. H. Ismail} [Anal. Appl., Singap. 1, No.~1, 129--140 (2003; Zbl 1042.33002)].
completely and absolutely monotonic-functions
scientific article; zbMATH DE number 2174970