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analyticity

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11: William P. Reinhardt
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. … 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. …
12: 2.4 Contour Integrals
If q ( t ) is analytic in a sector α 1 < ph t < α 2 containing ph t = 0 , then the region of validity may be increased by rotation of the integration paths. … is continuous in z c and analytic in z > c , and by inversion (§1.14(iii)) … Now assume that c > 0 and we are given a function Q ( z ) that is both analytic and has the expansion … Assume that p ( t ) and q ( t ) are analytic on an open domain 𝐓 that contains 𝒫 , with the possible exceptions of t = a and t = b . … in which z is a large real or complex parameter, p ( α , t ) and q ( α , t ) are analytic functions of t and continuous in t and a second parameter α . …
13: 10 Bessel Functions
14: 14 Legendre and Related Functions
15: 18 Orthogonal Polynomials
16: David M. Bressoud
His books are Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities, published in Memoirs of the American Mathematical Society 24, No. …
17: Ranjan Roy
18: Peter L. Walker
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. …
19: 5.2 Definitions
5.2.1 Γ ( z ) = 0 e t t z 1 d t , z > 0 .
When z 0 , Γ ( z ) is defined by analytic continuation. …
5.2.2 ψ ( z ) = Γ ( z ) / Γ ( z ) , z 0 , 1 , 2 , .
20: 4.7 Derivatives and Differential Equations
For a nonvanishing analytic function f ( z ) , the general solution of the differential equation
4.7.5 d w d z = f ( z ) f ( z )
4.7.6 w ( z ) = Ln ( f ( z ) ) +  constant .
4.7.12 d w d z = f ( z ) w
4.7.13 w = exp ( f ( z ) d z ) + constant .