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Mathematical Notes, 2021
The Newton interpretation of the psi function by rational functions with free poles is studied. A discrete formula for the Rodrigues determinants is obtained and the limit distribution of their zeros is found. The corresponding equilibrium problem of the theory of logarithmic potential is obtained.
V. N. Sorokin, V. N. Sorokin
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INEQUALITIES INVOLVING GAMMA AND PSI FUNCTIONS

Analysis and Applications, 2003
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.
Clark, W. Edwin, Ismail, Mourad E. H.
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A formula for the Chebyshev PSI function

Mathematical Notes of the Academy of Sciences of the USSR, 1978
A formula expressing the Chebyshevψ function in terms of the characteristic values of the Laplace-Beltrami operator on the fundamental domain of a modular group and the hyperbolic classes of conjugate elements of this group is derived.
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Sharp bounds for psi function

Applied Mathematics and Computation, 2015
In this paper, we present the greatest value a ? (1/15, ∞) and the least value b ? (4/15, ∞) such that the double inequality L ( x , a ) 0, where L ( x , a ) = 1 90 a 2 + 2 log ( x 2 + x + 3 a + 1 3 ) + 45 a 2 90 a 2 + 2 log ( x 2 + x + 15 a - 1 45 a ) and ?(x) is the classical psi function.
Yu-Ming Chu, Xiaohui Zhang, Zhen-Hang Yang +2 more
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