The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Chebyshev Formula

a formula for the approximate computation of a definite integral:

The formula is accurate for polynomials of degree not greater than n – 1, where n is the number of nodes. The values of the x_i have been computed for some n. In the case of n = 9, for example, x₁ = –x₉ = 0.911589, x₂ = –x₈ = 0.601019, x₃ = –x₇ = 0.528762, x₄ = –x₆ = 0.167906, and x₅ = 0. For n = 8 and n > 9, the x_i have complex values; the Chebyshev formula can therefore be used only for n = 1, 2, 3, 4, 5, 6, 7, and 9. The for mula was derived by P. L. Chebyshev in 1873.

Mentioned in

Approximate Integration

References in periodicals archive

The initial mechanism (links 0, 1) together with the fourth class second order structural group, which consists of a set of four links 2.5 (n=5) along with six kinematic pairs of the fifth class A, B, C, D, E, K ([p.sub.5]=6) form a fourth class mechanism with a degree of freeness equal to 1 according to the Chebyshev formula: W=3n-2[p.sub.5]-[p.sub.4], that is form a mechanism with one driving crank.

ANALYSIS OF FOURTH CLASS PLANE MECHANISMS WITH STRUCTURAL GROUPS OF LINKS OF THE SECOND ORDER

7 (n = 6) with nine kinematic pairs of 5th class--A, B, C, D, E, L, K, M, N ([p.sub.5] = 9) - forming the mechanism of the 4th class with degree of freedom 1 by Chebyshev formula (mechanism with a driving crank):

Analysis of fourth-grade flat machines with movable close-cycle formed by the rods and two complex links

(1) This formula is sometimes called Chebyshev formula, since in the one-dimensional case it is based on the expansion of a function in terms of Chebyshev polynomials [T.sub.i] of the first kind.

Spherical quadrature formulas with equally spaced nodes on latitudinal circles

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