Exponential Operators

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Proceedings of the Iowa Academy of Science, Vol: 47, Issue: 1, Page: 277-281

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Robertson, Fred
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Introduction. The non-commutative operational formula Dx = xD + 1, where D = d/dx, is well known. The difficulty of determining the order of the operations x and D in a function f (x, D) retarded the use of operative functions. Bourlet1 was the first to discover a way to express an operative function, f(x, D) such that the operations with D always precede those with x. Thus his operators obey the laws of algebra and their operational meaning is unique.