{"product_id":"the-functions-of-mathematical-physics-dover-books-on-physics-9780486652146","title":"The Functions of Mathematical Physics (Dover Books on Physics)","description":"\u003cp\u003eA 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 Laplaces 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 Hills equations  including the expansion theorems.\u003c\/p\u003e","brand":"My Store","offers":[{"title":"Default Title","offer_id":45951520473141,"sku":"ByrdShop_0486652149","price":241.61,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0627\/8139\/0901\/files\/9780486652146.jpg?v=1788111638","url":"https:\/\/atxbooks.com\/products\/the-functions-of-mathematical-physics-dover-books-on-physics-9780486652146","provider":"ATX Books","version":"1.0","type":"link"}