On the other hand, in , 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.
Now the kurtosis C(t) as well as the logarithmic derivative
of MSD [beta](t) can be computed.
Of late, with the development of Nevanlinna theory, Chiang and Feng  and Halburd and Korhonen  established independently those results about the difference analog of the lemma on the logarithmic derivative
, and there has been an increasing interest in studying complex difference equations.
It is well known that the pressure logarithmic derivative
curve has been used to identify true boundary model, but for multiphase flow well testing [13, 14], it is much more complicated, there is a great influence on pressure derivative due to the changes of fluid properties in the transition zone [15-17].
[psi](t) = [ln [GAMMA](t)]'t is the logarithmic derivative
of the gamma function.
Heittokangas, "Linear differential equations and logarithmic derivative
estimates," Proceedings of the London Mathematical Society.
So, the real part of its logarithmic derivative
is negative, and the second assertion of the theorem holds.
The condition of continuity of the logarithmic derivative
of the wave function on the boundary of the cylinder [rho] = R gives the equation
Lemmas 4 and 6 and the logarithmic derivative
lemma imply that, for i = 0, 1, ..., n and j = 0, 1, ..., m,
The digamma (or psi) function is defined for positive real numbers x as the logarithmic derivative
of Euler's gamma function, that is [psi](x) = d/dx ln[GAMMA](x) = [GAMMA]'(x)/[GAMMA](x).
Taking the logarithmic derivative
of the four recurrence relations and plugging in the initial conditions (14) gives the linear system