The Hypergeometric and Legendre Functions with Applications to Integral Equations of Potential Theory
Author: Chester Snow
Publisher:
Published: 1952
Total Pages: 336
ISBN-13:
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Author: Chester Snow
Publisher:
Published: 1952
Total Pages: 336
ISBN-13:
DOWNLOAD EBOOKAuthor: Chester Snow
Publisher:
Published: 1942
Total Pages: 338
ISBN-13:
DOWNLOAD EBOOKAuthor: Chester Snow
Publisher:
Published: 1952
Total Pages: 448
ISBN-13:
DOWNLOAD EBOOKAuthor: Chester Snow
Publisher:
Published: 1875
Total Pages: 348
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DOWNLOAD EBOOKAuthor: Chester Snow
Publisher:
Published: 1961
Total Pages: 427
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DOWNLOAD EBOOKAuthor: Chester Snow
Publisher:
Published: 1952
Total Pages: 450
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DOWNLOAD EBOOKAuthor: Nina Opanasivna Virchenko
Publisher: World Scientific
Published: 2001
Total Pages: 217
ISBN-13: 9810243537
DOWNLOAD EBOOKThe 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?(chà) etc.
Author: Harry Hochstadt
Publisher: Courier Corporation
Published: 2012-04-30
Total Pages: 354
ISBN-13: 0486168786
DOWNLOAD EBOOKA modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field — pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel — were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an n-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these — the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems.
Author: United States. Bureau of Standards
Publisher:
Published: 1944
Total Pages: 664
ISBN-13:
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Publisher:
Published: 1950
Total Pages: 650
ISBN-13:
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