Interpolation formula, Gauss

H - wi) = (xo xi) - H - wi) ( 2 i)-When the intervals between the two terms are large, or the differences between the various members of the series decrease rapidly, simple proportion cannot be used with confidence. To take away any arbitrary choice in the determination of the intermediate values, it is commonly assumed that the function can be expressed by a limited series of powers of one of the variables. Thus we have the interpolation formulas of Newton, Bessel, Stirling, Lagrange, and Gauss. 

BzzIntegra IGauss Based on the Gauss-Kronrod formulae. BzzIntegralGaussBF The interval is split into three subintervals. The lateral subintervals are very small and an interpolating polynomial based on Chebyshev points is adopted. The central interval is solved using the Gauss-Kronrod formulae. 

For computational purposes, the following formula for the Gauss-Jacobi quadrature weights can be obtained using the properties of the Lagrangian interpolation polynomials lj x)... 

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