On some relations between the laplace and mellin transforms

  • Authors:

  • J. S. Lew

  • Affiliations:

  • IBM Thomas J. Watson Research Center, Yorktown Heights, New York

  • Venue:
  • IBM Journal of Research and Development
  • Year:
  • 1975

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Abstract

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 ċ d/ds)n (1 + s)-1 with coefficients defined by the Mellin transform.