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An algorithm similar to Neville's algorithm for constructing the Lagrange interpolating polynomial. Let f(x|x_0,x_1,...,x_k) be the unique polynomial of kth polynomial order ...

An interpolation formula, sometimes known as the Newton-Bessel formula, given by (1) for p in [0,1], where delta is the central difference and B_(2n) = 1/2G_(2n) (2) = ...

(1) for p in [0,1], where delta is the central difference and E_(2n) = G_(2n)-G_(2n+1) (2) = B_(2n)-B_(2n+1) (3) F_(2n) = G_(2n+1) (4) = B_(2n)+B_(2n+1), (5) where G_k are ...

The difference between the measured or inferred value of a quantity x_0 and its actual value x, given by Deltax=x_0-x (sometimes with the absolute value taken) is called the ...

A term sometimes used to describe a map projection which is neither equal-area nor conformal (Lee 1944; Snyder 1987, p. 4).

An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the ...

A map projection defined by x = sin^(-1)[cosphisin(lambda-lambda_0)] (1) y = tan^(-1)[(tanphi)/(cos(lambda-lambda_0))]. (2) The inverse formulas are phi = sin^(-1)(sinDcosx) ...

Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

Series expansions of the parabolic cylinder functions U(a,x) and W(a,x). The formulas can be found in Abramowitz and Stegun (1972).