عنوان

Generalized associated Legendre functions and their applications /

(Number (ISBN

1281960721

(Number (ISBN

9781281960726

(Number (ISBN

9789812811783

(Number (ISBN

9812811788

Erroneous ISBN

9789810243531

Erroneous ISBN

9810243537

Title Proper

Generalized associated Legendre functions and their applications /

General Material Designation

[Book]

First Statement of Responsibility

Nina Virchenko, Iryna Fedotova.

Place of Publication, Distribution, etc.

River Edge, N.J. :

Name of Publisher, Distributor, etc.

World Scientific,

Date of Publication, Distribution, etc.

©2001.

Specific Material Designation and Extent of Item

1 online resource (xx, 195 pages) :

Other Physical Details

illustrations

Text of Note

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

Text of Note

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.

0

Text of Note

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.

Title

Generalized associated Legendre functions and their applications.

International Standard Book Number

9789810243531

Legendre's functions.

Legendre's functions.

MATHEMATICS-- Calculus.

MATHEMATICS-- Mathematical Analysis.

MAT-- 005000

MAT-- 034000

PBW

Number

Edition

Class number

Book number

Virchenko, N. O., (Nina Opanasivna)

Fedotova, Iryna.

Date of Transaction

20200823221303.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y