Let us teach this generalization of the final-value theorem

Abstract

It is shown that the previous [1-3] generalization of the final-value theorem to the average (not necessarily limiting) values, can be extended to the higher-order running averages ( t

Using Singularity Analysis to Approximate Transient Characteristics in Queueing Systems

“…The same two singularities as for the probability of an empty system may be dominant, namely z r = 1 and the square-root branchpoint z b of Y (z) as given in (14). The following expressions for the mean system content at the beginning of slot j are found:…”

On two generalisations of the final value theorem: scientific relevance, first applications, and physical foundations

“…Then (13) , that is, an infinite <f>, which is relevant to the discussion in [10], and for α < 1, we have <f> finite which is relevant to the discussion in [6].…”

“…The present work is motivated, on one side, by the appearance of the applications [1,2] and [3][4][5] of the generalization [6] of the Laplace transform final value theorem (FVT) [6][7][8][9], and, on the other side, by the more recent work [10] devoted to another generalization of the classical FVT. We discuss applications of both generalizations and explore the use of irrational functions in the last generalization.…”

“…The generalizations of [6] and [10] are very different, and for clarity, the notation GFVT is usually used only for the generalization of [6], as shown in Fig. 1.…”

“…This in no sense decreases the importance of the suggestions of [10], and in fact, the discussion of irrational functions influences the discussion of control systems (in section 2) and gives some support to the discussion of queueing theory (section 4) where sequences with non-integer powers arise. Teaching Laplace Transfom and its application to circuits/systems [6] [10] [1][2][3][4][5] [ [15][16][17] [9]…”