Khinal Parmar - Department of Basic Science and Humanities, NMIMS, MPSTME, Vile-Parle (West), Mumbai-۴۰۰۰۵۶, Maharashtra, India.
V. R. Lakshmi Gorty - Department of Basic Science and Humanities, NMIMS, MPSTME, Vile-Parle (West), Mumbai-۴۰۰۰۵۶, Maharashtra, India.

In this study, the quaternion Hankel transform is developed. Basic operational properties and inversion formula of quaternion Hankel transform are derived. Parseval’s relation for this transform is also established. The generalized quaternion Hankel transform is presented. In the concluding section, we demonstrate the application of the quaternion Hankel transform to Cauchy’s problem.

Hankel transform, Quaternion, Parseval's relation, generalization