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arXiv · 2407.13812

On the Laplace-type transform and its applications

Slobodan B. Tričković·Miomir S. Stanković
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Abstract

We use the Laplace transform and the Gamma function to introduce a new integral transform and name it the Laplace-type transform possessing the property of mapping a function to a functional sequence, which cannot be achieved by the Laplace transform. In addition, we construct a backward difference as a generalization of the backward difference operator $\nabla$, and connecting it to the Laplace-type transform, we deduce a method for solving difference equations and, relying on classical orthogonal polynomials, for obtaining combinatorial identities. A table of some elementary functions and their images is in the Appendix.

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Slobodan B. Tričković, Miomir S. Stanković. 2024-07-18. On the Laplace-type transform and its applications. https://arxiv.org/abs/2407.13812

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