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.

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 [4] and Halburd and Korhonen [5] 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