The barycentric interpolation formula can also easily be updated to incorporate a new node x _ { k + 1 } by dividing each of the w _ j, j = 0 \ dots k by ( x _ j-x _ { k + 1 } ) and constructing the new w _ { k + 1 } as above.
32.
Among other topics, Sarma specifically mentions the following : Tycho Brahe's reduction to the ecliptic, Newton-Gauss interpolation formula, Taylor series for sine and cosine functions, power series for sine and cosine functions, Lhuier's formula for the circum-radius of a cyclic quadrilateral, Gregory's series for the inverse tangent, and approximations to the value of pi.
