\chapter{~ Prologue}
\baselineskip 17pt

This book is motivated by the attempts to load at server mizugadro
the series of articles with definitions of terms related to the asymptotical analysis,
«Asymptotic»,
«Sectorial asymptotic»,
«Strip Asymptotic».
These concepts are imlicitely used in Mathematics and Physics at least since century 20,
but the definitions found at the free access sites seem to be not sufficient.
Among the sources available in the free access, the most complete seem to be the descriptions by 
Frank W.J. Olver and R. Wong
\cite{api,DLMF}.

In book «Superfunctions» 
\cite{r,e},  the concepts mentioned are used well beyond of the formal definitions.
The euristic style of that book implies, that some definitions and deductions are omitted - over-vice, the book would be of size of "Abramotits-Stegun",

This book appears ad bunch of definitions; all other can be considered as illustrations.
I try to follow the terminology from the publications cited, although the definitions are designed
to be used for complex values of the arguments of the functions.

Some colleagues qualify many things as «obvious» - until some contradictions appear.

In the informal discussion, at some scientific and near-scientific slang, words «by definition» are used
without referring to any definition of the term discussed.
Practically, in such a slang, words  «by definition» mean
«I do not know and I do not want to know he definition of this term, but I want you to accept my statement without discussion.»
Apparently, such an approach refers to the «motivated reasoning», so-called «Female logic» 
\cite{becklemishev,becklemishevE}.

I do not criticize such an approach. Perhaps, sometimes it is useful and even unavoidable in an euristical approach. But I still try to define the terms.