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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
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Any good books on numerical methods for ordinary differential equations?
Since nobody else has mentioned them, I will recommend Solving Ordinary Differential Equations (volumes I and II) by Hairer, Nørsett, and Wanner.
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Ewald's generalized theta function
A step by step derivation of Ewald summation can be found in:
Williams, D. E. (1971). Accelerated convergence of crystal-lattice potential sums. Acta Crystallographica Section A, 27(5), 452–455. doi: …