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On values of the psi function

Adam M., Piątek B., Pleszczyński M., Smoleń B., Wituła R.

Journal of Applied Mathematics and Computational Mechanics

2017

Vol. 16, nr 1

7--18

In the present paper, values of the psi function for many arguments connected with the golden ratio and Fibonacci numbers are determined or given in alternative form. Moreover, some integral representation of the psi function is found. This is a potential calculation base of values of the psi function for powers of argument. We also note that this integral representation gives better numerical estimation of values of the psi function than the respective Legendre’s integral formula.

An inequality involving the gamma and digamma functions

Qi F., Guo B.-N.

Journal of Applied Analysis

2016

Vol. 22, nr 1

49--54

In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.