analyticity
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11: William P. Reinhardt
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►Reinhardt is a theoretical chemist and atomic physicist, who has always been interested in orthogonal polynomials and in the analyticity properties of the functions of mathematical physics.
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►Reinhardt firmly believes that the Mandelbrot set is a special function, and notes with interest that the natural boundaries of analyticity of many “more normal” special functions are also fractals.
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12: 2.4 Contour Integrals
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►If is analytic in a sector containing , then the region of validity may be increased by rotation of the integration paths.
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►is continuous in and analytic in , and by inversion (§1.14(iii))
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►Now assume that and we are given a function that is both analytic and has the expansion
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►Assume that and are analytic on an open domain that contains , with the possible exceptions of and .
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►in which is a large real or complex parameter, and are analytic functions of and continuous in and a second parameter .
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13: 10 Bessel Functions
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14: 14 Legendre and Related Functions
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15: 18 Orthogonal Polynomials
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16: David M. Bressoud
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►His books are Analytic and Combinatorial
Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No.
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17: Ranjan Roy
18: Peter L. Walker
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►Walker’s published work has been mainly in real and complex analysis, with excursions into analytic number theory and geometry, the latter in collaboration with Professor Mowaffaq Hajja of the University of Jordan.
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