Данная книга является великолепным хендбуком для настоящих математиков. В данной книге собраны основные типы функций и методы работы с ними.
In 1964 the National Institute of Standards and Technology1 published the Handbook of Mathematical
Functions with Formulas, Graphs, and Mathematical Tables, edited by Milton Abramowitz
and Irene A. Stegun. That 1046-page tome proved to be an invaluable reference for the many scientists
and engineers who use the special functions of applied mathematics in their day-to-day work,
so much so that it became the most widely distributed and most highly cited NIST publication
in the rst 100 years of the institution's existence.2 The success of the original handbook, widely
referred to as \Abramowitz and Stegun" (\A&S"), derived not only from the fact that it provided
critically useful scienti c data in a highly accessible format, but also because it served to standardize
de nitions and notations for special functions. The provision of standard reference data of this type
is a core function of NIST.
Much has changed in the years since A&S was published. Certainly, advances in applied mathematics
have continued unabated. However, we have also seen the birth of a new age of computing
technology, which has not only changed how we utilize special functions, but also how we communicate
technical information. The document you are now holding, or the Web page you are now
reading, represents an e ort to extend the legacy of A&S well into the 21st century. The new
printed volume, the NIST Handbook of Mathematical Functions, serves a similar function as the
original A&S, though it is heavily updated and extended. The online version, the NIST Digital
Library of Mathematical Functions (DLMF), presents the same technical information along with
extensions and innovative interactive features consistent with the new medium. The DLMF may
well serve as a model for the e ective presentation of highly mathematical reference material on the
Web.
The production of these new resources has been a very complex undertaking some 10 years in
the making. This could not have been done without the cooperation of many mathematicians,
information technologists, and physical scientists both within NIST and externally. Their unfailing
dedication is acknowledged deeply and gratefully. Particular attention is called to the generous
support of the National Science Foundation, which made possible the participation of experts from
academia and research institutes worldwide.