Smoothing functions play an important role in Support Vector Machine(SVM).This paper derived an important recursive formula and a new class of smoothing functions using the technique of interpolation functions.Thus the problem of seeking better smoothing functions was solved

which has been a major obstacle in this field for a long time.Several of its important properties were discussed.It was shown that the approximation accuracy of interpolation functions is better than the integral of the sigmoid function by an order of magnitude.It is also obviously higher than those of the first /second-order smooth polynomial functions.Therefore

the proposed class of interpolation functions is a competitive candidate for smoothing SVM.