  We present a new formula for divided difference and few new schemes of
divided difference tables in this paper. Through this, we derive new
interpolation, numerical differentiation and numerical integration formulas
with arbitrary order of accuracy for evanly and unevanly spaced data. First, we
study the new interpolation formula which generalizes both Newton's and
Lagrange's interpolation formula with the new divided difference table for
unevanly spaced points and using this; we derive other interpolation formulas,
in terms of differences for evanly spaced data. Second, we study two new
different methods of numerical differentiation for both evanly and unevanly
spaced points without differentiating the interpolating polynomials or the use
of operators. Third, we derive new numerical integration formulas using new
differentiation formulas and Taylor formula for both evanly and unevanly spaced
data. Basic computer algorithms for few new formulas are given. In Comparison
to former polynomial interpolation, numerical differentiation and numerical
integration formuals, these new formulas have some featured advantages for
approximating functional values, numerical derivatives of higher order and
approximate integral values for evanly and unevanly spaced data.
