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Exploring Integration by Differentiation
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Exploring Integration by Differentiation
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This work validates and extends the method of integration by differentiation, initially introduced by A. Kempf et al., and demonstrates its compatibility with classical rules of integration. It provides applications to classical integrals, including one by Ramanujan, and extends the method to the multivariate setting. Volumes of simplexes are computed by acting with indicator functions on elementary kernels, and a rotationally invariant formulation is derived. Finally, the method is extended to Jackson's q-integral.
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Cited by 1 Pith paper
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Learning from Ramanujan: Elementary Approaches to Profound Ideas
Elementary proofs and modest extensions are supplied for selected Ramanujan notebook entries using classical tools.
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