WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 24, 2025
Special Relationships between Integral Transformations and Improper Integrals, along with some of Their Extensive Implications
Author:
Abstract: In this special note, an extensive improper integral, which possesses the form given by $$ \int_{0}^{∞} v(τ)e^{-λu(τ)}$$ dt, will initially be considered, where the function v(τ) both is (piecewise) continuous on the interval [0, ∞) and possesses an exponential order α on [0,∞), and also $$ λ∈ \mathbb{C}-0, \Re e(λ)>α $$ and, for all $$τ∈[0, ∞), u(τ)>0$$. Various relationships of that special integral with diverse special functions and transformations will subsequently be created, and some implications of these special relationships will also be pointed out.