letter: development of general functional form of the gravitational potential: addressing the flatness problem in galactic rotation curves

This letter presents a mathematical model that may help address the long-standing problem of galaxy rotation curves. the strategy involves exploring the variation of circular velocity `ν’ with respect to radial distance `r’ as a result of which a bessel differential equation is developed, yielding a general functional form of the potential as a bessel function. employing this potential in the case of galaxies, we find the velocity profile in terms of bessel functions. this approach establishes bessel functions as a powerful choice for investigating galactic rotation and deepening our understanding of the universe.