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The Functions of Mathematical Physics (Dover Books on Physics & Chemistry)

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The Functions of Mathematical Physics (Dover Books on Physics & Chemistry) Cover

 

Synopses & Reviews

Publisher Comments:

A 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.

Synopsis:

Comprehensive treatment of orthogonal polynomials, hypergeometric functions, Hill's equation, much more. Bibliography. Index.

Synopsis:

Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.

Synopsis:

Comprehensive textbook provides both mathematicians and applied scientists with a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation. Lucid and useful presentations for anyone working in pure or applied mathematics or physics.

Product Details

ISBN:
9780486652146
Author:
Hochstadt, Harry
Publisher:
Dover Publications
Location:
New York :
Subject:
Science
Subject:
Physics
Subject:
Mathematical Physics
Subject:
Functions, special
Subject:
Orthogonal polynomials.
Subject:
gamma function
Subject:
Hypergeometric functions.
Subject:
Physics-Math
Subject:
Physics-General
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Physics & Chemistry
Series Volume:
no. 37
Publication Date:
20120231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
352
Dimensions:
8.5 x 5.38 in 0.81 lb

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Related Subjects


Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Physics
Science and Mathematics » Physics » General
Science and Mathematics » Physics » Math

The Functions of Mathematical Physics (Dover Books on Physics & Chemistry) Used Trade Paper
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Product details 352 pages Dover Publications - English 9780486652146 Reviews:
"Synopsis" by , Comprehensive treatment of orthogonal polynomials, hypergeometric functions, Hill's equation, much more. Bibliography. Index.

"Synopsis" by ,
Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.
"Synopsis" by ,
Comprehensive textbook provides both mathematicians and applied scientists with a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation. Lucid and useful presentations for anyone working in pure or applied mathematics or physics.
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