An update on the Upadhyaya transform ∗
DOI:
https://doi.org/10.48165/Keywords:
Upadhyaya transform, n-dimensional Upadhyaya transform, degener ate Upadhyaya transform, Dinesh Verma transform, Raj transform, β-Laplace transformAbstract
It is almost two years now when the Upadhyaya transform was introduced by the first author (Upadhyaya, Lalit Mohan, Introducing the Upadhyaya integral trans form, Bull. Pure Appl. Sci. Sect. E Math. Stat., 38(E)(1), 471–510, doi 10.5958/2320- 3226.2019.00051.1 https://www.researchgate.net/publication/334033797)) as the
most powerful, versatile and robust generalization and unification of a number of variants of the classical Laplace transform which have appeared in the mathematics research litera ture during the years 1993 to 2019. In this paper we provide an update on the Upadhyaya transform, where we explain the definition the one-dimensional Upadhyaya transform and its n-dimensional generalization in more detail and we show that how many other various variants of the classical Laplace transform, that have come to our notice since then and most of which are introduced into the mathematics research literature during the past two years by a number of authors after the advent of the Upadhyaya transform, follow as a special case of the Upadhyaya transform. We find the Upadhyaya transform of some trigonometric and hyperbolic functions, the sine integral, the generalized hypergeometric function and the Bessel function of the first kind in order to exemplify the vast power of the Upadhyaya transform and we also correct a minor typo in the aforementioned paper of the first author.
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