A generalization of the Widder potential transform and applications


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Dernek N., Kurt V., ŞİMŞEK Y., Yurekli O.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, vol.22, no.6, pp.391-401, 2011 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 6
  • Publication Date: 2011
  • Doi Number: 10.1080/10652469.2010.513110
  • Journal Name: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.391-401
  • Keywords: Laplace transforms, L(2)-transforms, Widder potential transforms, Glasser transforms, P(v,2)-transforms, Hankel transforms, K(v)-transforms, Parseval-Goldstein-type theorems, IDENTITIES, L-2-TRANSFORM
  • Akdeniz University Affiliated: Yes

Abstract

In the present paper, the authors consider the P(v,2)-transform as a generalization of the Widder potential transform and the Glasser transform. The P(v,2)-transform is obtained as an iteration of the L(2)-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.