Abstract
We derive asymptotic expansions of the Poisson transform of a locally integrable function f(t): \((\sqrt{4\pi t})^{-1}\int_{-\infty}^{\infty}\exp \lbrace{-(x-y)^{2}/(4t)}\rbrace f(y) \,dy\), for small and large t. All the expansions are accompanied by error bounds for the remainder at any order of the approximation.
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The financial support of Sec. Est. Educ. y Univ. (Programa Salvador de Madariaga, res. 09/03/04) and the Dirección General de Ciencia y Tecnología (REF. MTM2004-05221) are acknowledged.
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Ferreira, C., López, J.L. Approximations of the Poisson transform for large and small values of the transformation parameter. Ramanujan J 30, 309–326 (2013). https://doi.org/10.1007/s11139-012-9438-y
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DOI: https://doi.org/10.1007/s11139-012-9438-y