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IBM Journal of Research and Development  
Volume 19, Number 6, Page 582 (1975)
Nontopical Issue
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On Some Relations between the Laplace and Mellin Transforms

by J. S. Lew
Several earlier papers have applied some identities relating the Laplace and Mellin transforms; this note develops certain such identities, achieving greater generality and rigor. Specifically each of these transforms is expressed as a contour integral involving the other, and an expansion of the Laplace transform is derived in terms of the functions (s • d/ds) n (1 + s)−1 with coefficients defined by the Mellin transform.
Related Subjects: Computational methods; Mathematics