In the 00th and 00th centuries, scientists discovered That the elementary functions - Powers, roots, trigonometric functions and Their inverses - HAD Their limitations. They found solutions for some Important That physical problems - like the orbital motion of planets, the oscillatory motion of suspended chains, and the calculation of the gravitational potential of Nearly spherical bodies - Could not always be Described in a closed form using only elementary functions. Even in the realm of pure mathematics, some quantities - the circumference of: such as an ellipse - Were Also impossible to discuss in terms Such. Describing Functions These solutions to problems Were Often Expressed as infinite series, integrals as, or as solutions to differential equations