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A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions

2019
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Axioms
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The purpose of this note is to provide an expository introduction to some more curious integral formulas and transformations involving generating functions. We seek to generalize these results and integral representations which effectively provide a mechanism for converting between a sequence's ordinary and exponential generating function (OGF and EGF, respectively) and vice versa. The Laplace transform provides an integral formula for the EGF-to-OGF transformation, where the reverse OGF-to-EGF

doi:10.3390/axioms8020062
fatcat:ozpuus3v5zeq5cled7bfenl7xi