analyticity
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31—40 of 153 matching pages
31: 27.18 Methods of Computation: Primes
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►An analytic approach using a contour integral of the Riemann zeta function (§25.2(i)) is discussed in Borwein et al. (2000).
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32: Roderick S. C. Wong
33: 32.2 Differential Equations
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►be a nonlinear second-order differential equation in which is a rational function of and , and is locally analytic in , that is, analytic except for isolated singularities in .
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►in which , , , , and are locally analytic functions.
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34: 4.14 Definitions and Periodicity
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4.14.7
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35: 33.2 Definitions and Basic Properties
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§33.2(i) Coulomb Wave Equation
… ►§33.2(ii) Regular Solution
… ► is a real and analytic function of on the open interval , and also an analytic function of when . … ►As in the case of , the solutions and are analytic functions of when . Also, are analytic functions of when . …36: 33.14 Definitions and Basic Properties
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§33.14(i) Coulomb Wave Equation
… ►§33.14(ii) Regular Solution
… ► is real and an analytic function of in the interval , and it is also an analytic function of when . … ►§33.14(iii) Irregular Solution
… ► is real and an analytic function of each of and in the intervals and , except when or . …37: 1.9 Calculus of a Complex Variable
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Analyticity
… ►A function is analytic in a domain if it is analytic at each point of . A function analytic at every point of is said to be entire. … ► …38: 14.31 Other Applications
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►Applications of toroidal functions include expansion of vacuum magnetic fields in stellarators and tokamaks (van Milligen and López Fraguas (1994)), analytic solutions of Poisson’s equation in channel-like geometries (Hoyles et al. (1998)), and Dirichlet problems with toroidal symmetry (Gil et al. (2000)).
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39: 28.19 Expansions in Series of Functions
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►Let be a normal value (§28.12(i)) with respect to , and be a function that is analytic on a doubly-infinite open strip that contains the real axis.
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40: 33.13 Complex Variable and Parameters
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►These functions may also be continued analytically to complex values of , , and .
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