Abstract
Euler invented integral transforms in the context of second order differential equations. He used them in a fragment published in 1763 and in a chapter of Institutiones Calculi Integralis (1769). In introducing them he made use of earlier work in which a concept akin to the integral transform is implicit. It would, however, be reading too much into that earlier work to see it as contributing to the theory of the integral transform. Other work sometimes cited in this context in fact has different concerns.
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Deakin, M.A.B. Euler's invention of integral transforms. Arch. Hist. Exact Sci. 33, 307–319 (1985). https://doi.org/10.1007/BF00348586
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DOI: https://doi.org/10.1007/BF00348586