Bessel function of the first kind

The Bessel function of the first kind is a special mathematical function that arises when solving certain types of differential equations, especially those involving circular or cylindrical symmetry, such as vibrations of a drum, heat conduction in a cylinder, or electromagnetic waves in cylindrical structures. It describes how a quantity oscillates or behaves in systems with circular geometry. These functions are characterized by oscillatory patterns similar to sine and cosine but adjusted to fit the boundary conditions of cylindrical problems. They are fundamental in physics and engineering for modeling wave-like phenomena in circular or cylindrical contexts.