Mohammad Ali Jafari - Financial Mathematics Department, Finance Faculty, Kharazmi University, Tehran, Iran
Azim Aminataei - Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

In this work, using the determination function, some new kinds of interpolation formulas are presented.These novel formulas are extensions of Lagrange interpolation. Error formula for these new kind of interpolation formulas are obtained. Finally, using these formulas, some new numerical integration formulas in closed-type and open-type are presented. Absolute error of quadrature formulas show the efficiency of the proposed formulas.

Interpolation formula, Error formula, Numerical integration