A widely applicable class of infinite series is known as the set of all power series. It is already established since the middle of the 17th century where and when the infinitesimal calculus was contemporaneously discovered by both Newton and Leibniz that many useful rational, transcendental, and circular functions can be expanded using power series. Three examples are ��/(1+��), ℯⁿ, and ������(��). The first was given earlier. The second is given by 1+��/1!+��²/2!+…+��ⁿ/��!+… (for all ��). The third is given by ��-��³/3!+��⁵/5!-��⁷/7!+…+(-1)ⁿ��²ⁿ⁺¹/(2��+1)!+… (for all ��). All these have each term’s denominator as product of positive integers. However, the infinite series expansion to which ��-th partial sum is given by the rational function ��/(1+��) has its ��-th term given by 1/��(1+��).

From the perspective of Newton’s point force mechanics, the unique expression 1/��(1+��) signifies a physical equivalence to the inverse square law of the gravitational force, the Coulomb’s force, and the Biot-Savart’s magnetic intensity at a point of spacetime. This becomes more and more exactly equivalent for larger and larger values of the independent variable such that as �� approaches infinity 1/��(1+��) approaches 1/��² where �� is the physical equivalent to �� as the distance separating between any given 2-point force configuration of physical reality. It validates the long range effectiveness of both gravitational and electromagnetic forces but does not indicate the unification hindered by differences of the coupling constants understandable by a theory of gauge invariance.