Special Functions & Their Applications 英文原版 特殊函数及其应用 N. N. Lebedev

基本信息

Author N. N. Lebedev

Format Paperback | 336 pages

Dimensions 135 x 214 x 16.26mm | 322.05g

Publication date 01 Jun 1972

Publisher Dover Publications Inc.

Publication City/Country New York, United States

Language English

Edition Revised

Edition Statement Revised ed.

Illustrations note 38 figures

ISBN10 0486606244

ISBN13 9780486606248

页面参数仅供参考，具体以实物为准

内容简介

理查德·西尔弗曼（Richard Silverman）的新译本为英国读者提供了当代俄罗斯著名数学家NN列别杰夫（NN Lebedev）的作品。尽管有大量有关特殊功能的论文可供使用，但这些对学生或应用数学家以及Lebedev的入门级实践指导方法均无济于事。他对更重要的特殊功能的基础理论的系统处理，以及该理论在物理学和工程学中特定问题上的应用，为学生以及与实际数学应用或使用有关的人员使用特殊功能提供了实践课程。考虑到覆盖范围的实用性，大多数空间都用于圆柱函数的应用，尤其是球谐函数的应用。列别捷夫 但是，也要详细处理：伽玛函数，概率积分和相关函数，指数积分和相关函数，考虑了勒让德，埃尔米特和拉盖尔多项式的正交多项式（对扩展一系列函数的技术进行了特殊处理） Hermite和Laguerre多项式），Airy函数，超几何函数（使理论物理学家可以访问这通常很小的区域）以及抛物柱面函数。各个章节中材料的安排在一定程度上使本书的不同部分彼此独立。尽管需要熟悉复杂变量理论，但已经进行了认真的尝试，以使该领域所需的背景知识降至*低。在相应章节结尾的问题中，将发现未出现在正文中的特殊功能的各种有用属性。该版本与修订的俄文版本（莫斯科，1965年）非常相似。但是，理查德·西尔弗曼（Richard Silverman）使这本书对英语阅读者更加有用。参考书目和参考文献已偏向于英语或西欧语言版本的书籍，并且此版本中还添加了许多其他问题。

Richard Silverman's new translation makes available to English readers the work of the famous contemporary Russian mathematician N. N. Lebedev. Though extensive treatises on special functions are available, these do not serve the student or the applied mathematician as well as Lebedev's introductory and practically oriented approach. His systematic treatment of the basic theory of the more important special functions and the applications of this theory to specific problems of physics and engineering results in a practical course in the use of special functions for the student and for those concerned with actual mathematical applications or uses. In consideration of the practical nature of the coverage, most space has been devoted to the application of cylinder functions and particularly of spherical harmonics. Lebedev, however, also treats in some detail: the gamma function, the probability integral and related functions, the exponential integral and related functions, orthogonal polynomials with consideration of Legendre, Hermite and Laguerre polynomials (with exceptional treatment of the technique of expanding functions in series of Hermite and Laguerre polynomials), the Airy functions, the hypergeometric functions (making this often slighted area accessible to the theoretical physicist), and parabolic cylinder functions. The arrangement of the material in the separate chapters, to a certain degree, makes the different parts of the book independent of each other. Although a familiarity with complex variable theory is needed, a serious attempt has been made to keep to a minimum the required background in this area. Various useful properties of the special functions which do not appear in the text proper will be found in the problems at the end of the appropriate chapters. This edition closely adheres to the revised Russian edition (Moscow, 1965). Richard Silverman, however, has made the book even more useful to the English reader. The bibliography and references have been slanted toward books available in English or the West European languages, and a number of additional problems have been added to this edition.