عنوان

Generalized associated Legendre functions and their applications /

شابک

1281960721

شابک

9781281960726

شابک

9789812811783

شابک

9812811788

شابک اشتباه

9789810243531

شابک اشتباه

9810243537

عنوان اصلي

Generalized associated Legendre functions and their applications /

نام عام مواد

[Book]

نام نخستين پديدآور

Nina Virchenko, Iryna Fedotova.

محل نشرو پخش و غیره

River Edge, N.J. :

نام ناشر، پخش کننده و غيره

World Scientific,

تاریخ نشرو بخش و غیره

©2001.

نام خاص و کميت اثر

1 online resource (xx, 195 pages) :

ساير جزييات

illustrations

متن يادداشت

Includes bibliographical references (pages 183-191) and index.

متن يادداشت

1. A general information on Legendre functions -- 2. The generalized associated Legendre functions -- 3. The series representations of the generalized associated Legendre functions -- 4. Relations between different solutions of the generalized Legendre equation. Wronskians of linearly independent solutions -- 5. Relations between contiguous generalized associated Legendre functions -- 6. Differential operators generated by the generalized associated Legendre equation -- 7. Asymptotic formulas for the generalized associated Legendre functions in a neighborhood of singular points -- 8. Asymptotic representations of the generalized associated Legendre functions as functions of parameters -- 9. Integral representations of the generalized associated Legendre functions of the first kind -- 10. Integral representations of the generalized associated Legendre functions of the second kind -- 11. Zeros of the generalized associated Legendre functions -- 12. Connection of the generalized associated Legendre functions with the Jacobi functions -- 13. Integral relations and series with the generalized associated Legendre functions -- 14. Relations between the generalized associated Legendre functions, Bessel functions, elliptic integrals and incomplete B-functions -- 15. Integral transforms with the generalized associated Legendre functions.

بدون عنوان

0

متن يادداشت

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 "YFq", 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 Legendre functions of the first and the second kind, "Pm, nN(Z)" and "Qm, nN(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 Legendre functions as their series representations, asymptotic formulas in a neighbourhood 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, nN(Z)" and "Qm, nN(Z)", the classes of dual and triple integral equations associated with the function "Pm, n-1/2+/omega(chdelta)" etc.

عنوان

Generalized associated Legendre functions and their applications.

شماره استاندارد بين المللي کتاب و موسيقي

9789810243531

موضوع مستند نشده

Legendre's functions.

موضوع مستند نشده

Legendre's functions.

موضوع مستند نشده

MATHEMATICS-- Calculus.

موضوع مستند نشده

MATHEMATICS-- Mathematical Analysis.

موضوع مستند نشده

MAT-- 005000

موضوع مستند نشده

MAT-- 034000

موضوع مستند نشده

PBW

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Virchenko, N. O., (Nina Opanasivna)

مستند نام اشخاص تاييد نشده

Fedotova, Iryna.

تاريخ عمليات

20200823221303.0

قواعد فهرست نويسي ( بخش توصيفي )

pn

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y