A generalization of the Widder potential transform and applications

Abstract

In the present paper, the authors consider the 𝒫_{ν, 2}-transform as a generalization of the Widder potential transform and the Glasser transform. The 𝒫_{ν, 2}-transform is obtained as an iteration of the ℒ₂-transform with itself. Many identities involving these transforms are given. By making use of these identities, a number of new Parseval–Goldstein-type identities are obtained for these and many other well-known integral transforms. The identities proved in this paper are shown to give rise to useful corollaries for evaluating infinite integrals of special functions. Some examples are also given as illustration of the results presented here.

Keywords:

• Laplace transforms
• ℒ₂-transforms
• Widder potential transforms
• Glasser transforms
• 𝒫_ν2-transforms
• Hankel transforms
• 𝒦_ν-transforms
• Parseval–Goldstein-type theorems

2010 Mathematics Subject Classification :

• Primary 44A10
• 44A15
• Secondary 33C10
• 44A35