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11: 1.10 Functions of a Complex Variable
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►The series (1.10.6) converges uniformly and absolutely on compact sets in the annulus.
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►For each , is analytic in ; is a continuous function of both variables when and ; the integral (1.10.18) converges at , and this convergence is uniform with respect to in every compact subset of .
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►where is analytic for all , and the convergence of the product is uniform in any compact subset of .
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12: 28.32 Mathematical Applications
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►defines a solution of Mathieu’s equation, provided that (in the case of an improper curve) the integral converges with respect to uniformly on compact subsets of .
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13: Bibliography P
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Stacking models of vesicles and compact clusters.
J. Statist. Phys. 80 (3–4), pp. 755–779.
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14: 1.9 Calculus of a Complex Variable
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Term-by-Term Integration
►Suppose the series , where is continuous, converges uniformly on every compact set of a domain , that is, every closed and bounded set in . … ►Suppose converges uniformly in any compact interval in , and at least one of the following two conditions is satisfied: …15: 13.8 Asymptotic Approximations for Large Parameters
16: 18.18 Sums
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►Moreover, the series (18.18.2) converges uniformly on any compact domain within .
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►Then (18.18.2), with replaced by , applies when ; moreover, the convergence is uniform on any compact interval within .
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►The convergence of the series (18.18.4) is uniform on any compact interval in .
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►The convergence of the series (18.18.6) is uniform on any compact interval in .
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17: 20.5 Infinite Products and Related Results
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►With the given conditions the infinite series in (20.5.10)–(20.5.13) converge absolutely and uniformly in compact sets in the -plane.
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18: 21.2 Definitions
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►This -tuple Fourier series converges absolutely and uniformly on compact sets of the and spaces; hence is an analytic function of (each element of) and (each element of) .
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19: 18.15 Asymptotic Approximations
20: Bibliography K
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Compact quantum groups and -special functions.
In Representations of Lie Groups and Quantum Groups,
Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.
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