# Identities for the Ln-transform, the L2n-transform and the P2n transform and their applications

**Authors:** Nese Dernek, Fatih Aylikci  
**arXiv:** [1403.2188](https://arxiv.org/abs/1403.2188)  
**Date:** 2014-03-10  
**Summary page:** https://www.summarizepaper.com/en/paper/1403.2188v1/

## Key points

- Nese Dernek and Fatih Aylikci introduce new integral transforms that generalize the Laplace and Stieltjes transforms
- The new transforms include Ln-transform, L2n-transform, and P2n-transform
- The second iterate of the L2n-transform is equivalent to the P2n-transform
- New Parseval-Goldstein type identities are derived from this relationship, which can be used to evaluate infinite integrals of special functions
- The paper provides illustrative examples to further explain their findings
- This work has significant implications in mathematical analysis and can be applied to various fields such as physics, engineering, and finance
- The paper contributes to advancing our understanding of integral transforms by introducing new variations on existing ones and providing novel relationships between them.

## Summary

In their paper titled "Identities for the Ln-transform, the L2n-transform and the P2n transform and their applications," Nese Dernek and Fatih Aylikci introduce several new integral transforms that generalize the classical Laplace and Stieltjes transforms. These include the Ln-transform, L2n-transform, and P2n-transform. The authors demonstrate that the second iterate of the L2n-transform is equivalent to the P2n-transform. By leveraging this relationship, they derive a few new Parseval-Goldstein type identities which provide useful relations for evaluating infinite integrals of special functions. To further illustrate their findings, they also present related illustrative examples. This work has significant implications in mathematical analysis and can be applied to various fields such as physics, engineering, and finance. Overall, this paper contributes to advancing our understanding of integral transforms by introducing new variations on existing ones and providing novel relationships between them. The resulting identities have practical applications in solving complex mathematical problems involving special functions.