A Novel Form of Multiplicative Gamma Function and Its Analytical Properties

In this article, we introduce and investigate a novel Euler‐style multiplicative gamma function formulated within the framework of multiplicative calculus. This function is defined via a multiplicative integral and serves as a multiplicative analogue of the classical gamma function. We establish its convergence, continuity, strict positivity, and multiplicative differentiability for all positive real inputs. Additionally, we derive the function′s asymptotic behavior and demonstrate that it exhibits subexponential growth, in contrast to the factorial‐like divergence of the classical gamma function. Analytical comparisons and numerical examples are provided to highlight the distinct characteristics and advantages of the new function. Applications are discussed in contexts such as multiplicative number theory, population dynamics, and information systems, where modeling based on proportional changes is more appropriate than additive frameworks. The results open new directions in the theory of multiplicative special functions and their use in modeling real‐world multiplicative phenomena.