Generalized associated legendre functions and their applications
著者
書誌事項
Generalized associated legendre functions and their applications
World Scientific, c2001
大学図書館所蔵 全12件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliography (p. 183-191) and index
内容説明・目次
内容説明
The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions Fq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,n (z) and Qm,n (z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,n (z) and Qm,n (z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+i (ch ) etc.
目次
- A General Information on Legendre Functions
- The Generalized Associated Legendre Functions
- The Series Representations of the Generalized Associated Legendre Functions
- Relations Between Different Solutions of the Generalized Legendre Equation. Wronskians of Linearly Independent Solutions
- Relations Between Contiguous Generalized Associated Legendre Functions
- Differential Operators Generated by the Generalized Associated Legendre Equation
- Asymptotic Formulas for the Generalized Associated Legendre Functions in a Neighborhood of Singular Points
- Asymptotic Representations of the Generalized Associated Legendre Functions as the Functions of Parameters
- Integral Representations of the Generalized Associated Legendre Functions of the First Kind
- Integral Representations of the Generalized Associated Legendre Functions of the Second Kind
- Zeros of the Generalized Associated Legendre Functions
- Connection of the Generalized Associated Legendre Functions with the Jacobi Functions
- and other topics.
「Nielsen BookData」 より