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This is a discussion of miscellaneous summation, integration and transformation formulas obtained using Fourier analysis. The topics covered are: Series of the form ₍ cₙe^ i n²; Fusion of integrals, and in particular fusion of q-beta integrals related to Gauss-Fourier transform, and a related family of eigenfunctions of the cosine Fourier transform; Summation formulas of the type ₍ ₁ (n) n\, (n) with Dirichlet characters; Trigonometric Fourier series expansion of hypergeometric functions of the argument ²x; Modifications of the inverse tangent integral and identities for corresponding infinite products.
Martin Nicholson (Tue,) studied this question.
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