1) In diction, dialect and style it is obviously dependent upon Homer, and is therefore considerably later than the "Iliad" and "Odyssey": moreover, as we have seen, it is in revolt against the romantic school, already grown decadent, and while the
digamma is still living, it is obviously growing weak, and is by no means uniformly effective.
I don't care a straw for Greek particles, or the
digamma; no more does his mother.
On the other hand, in [8], we showed that the double cotangent function [Cot.sub.2](x, (1,[tau])) (the logarithmic derivative of the double sine function) degenerates to the
digamma function (the logarithmic derivative of the gamma function) as [tau] tends to infinity.
Strumia, "Interpreting the 750 GeV
digamma excess: a review," High Energy Physics--Phenomenology, 2016, https:// arxiv.org/abs/1605.09401.
involving the
digamma function y that has no singularities and starts with the power n.
The above notion of Schur convexity was first introduced by Schur in 1923 and has many important applications in analytic inequalities [16-20], isoperimetric problem for polytopes [21], linear regression [22], combinatorial optimization [23], graphs and matrices [24], gamma and
digamma functions [25], information-theoretic topics [26], stochastic orderings [27], and other related fields.
Notations f(*): Probability density function E(*): Mean function Var(*): Variance function [gamma](y, x): Lower incomplete gamma function [GAMMA](y, x): Upper incomplete gamma function F(*): Cumulative distribution function S(*): Survival function h(*): Hazard rate function L(*): Likelihood function l(*): Log-likelihood function [psi](*):
Digamma function [psi]'(*): Trigamma function I(*): Expected Fisher information matrix [mu]: Positive parameter [phi]: Positive parameter [alpha]: Positive parameter [beta]: Real parameter [lambda]: Positive parameter Q(*): Quantile function [THETA]: Vector of parameters H(*: Observed Fisher information matrix [[mu].sub.k]: kth moment G(*: TTT-plot [D.sub.n]: Kolmogorov-Smirnov statistic [y.sup.*]: Predictive value.
[psi](*) is the
digamma function and [mathematical expression not reproducible].
where [psi](x) is the
digamma function defined as [psi]([theta]) = ([partial derivative]/[partial derivative][theta]) log [GAMMA]([theta]).
ML-based m parameter estimation problem reduces to the problem of solving some transcendental equations written in the form of logarithmic and
digamma functions.
where B(a, b) = [GAMMA](a) [GAMMA] (b)/ [GAMMA] (a + b) and [PSI](x)is the
digamma function, the asymptotic expression of SOP at high MER can be written as