Description 
1 online resource (xx, 195 pages) : illustrations 
Contents 
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 Bfunctions  15. Integral transforms with the generalized associated Legendre functions 
Summary 
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 wellknown 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 integrodifferential properties of the functions "Pm, nN(Z)" and "Qm, nN(Z)", the classes of dual and triple integral equations associated with the function "Pm, n1/2+/omega(chdelta)" etc 
Bibliography 
Includes bibliographical references (pages 183191) and index 
Notes 
Print version record 
Subject 
Legendre's functions.


MATHEMATICS  Calculus.


MATHEMATICS  Mathematical Analysis.


Legendre's functions

Form 
Electronic book

Author 
Fedotova, Iryna.

ISBN 
9789812811783 

9812811788 

1281960721 

9781281960726 
