On the Birkhoff Quadrature Formulas Using Even and Odd Order of Derivatives

الملخص EN

We introduce some New Quadrature Formulas byusing Jacoby polynomials and Laguerre polynomials.

These formulas can beobtained for a finite and infinite interval and also separately for the even or oddorder of derivatives.

By using the properties of error functions of the aboveorthogonal polynomials we can obtain the error functions for these formulas.

Application of the new approaches increases their precision degrees.

Finally,some examples are given to illuminate the details.