A New Kind of Infinite Series and Its Applications on Neural Networks

A new important theorem for function expansion and a new infinite series based on the new expansion is proposed. Unlike constant derivatives at a point by Taylor's expansion, the terms are functions associated with derivatives. The expansion generated by a function is not the form of polynomials, which is different from Taylor's expansion. Some application examples are given to show that the region of convergence is much larger than that obtained by Taylor's Series. As a kind of application, a new learning algorithm based on the new expansion for training neural networks is also proposed. The weight functions using the new expansion are more suitable for training those patterns obtained by some rational problems.