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Let f(x) be differentiable on the open interval (a,b) and continuous on the closed interval [a,b]. Then there is at least one point c in (a,b) such that ...

For an infinite population with mean mu, variance sigma^2, skewness gamma_1, and kurtosis excess gamma_2, the corresponding quantities for the distribution of means are ...

The mean clustering coefficient of a graph G is the average of the local clustering coefficients of G. It is implemented in the Wolfram Language as ...

The mean tetrahedron volume V^_ is the average volume of a tetrahedron in tetrahedron picking within some given shape. As summarized in the following table, it is possible to ...

The mean triangle area A^_ is the average area of a triangle in triangle picking within some given shape. As summarized in the following table, it is possible to compute the ...

The extended mean-value theorem (Anton 1984, pp. 543-544), also known as the Cauchy mean-value theorem (Anton 1984, pp. 543) and Cauchy's mean-value formula (Apostol 1967, p. ...

The mean square displacement (MSD) of a set of N displacements x_n is given by <|x|^2>=sum_(k=1)^N|x_k|^2. It arises particularly in Brownian motion and random walk problems. ...

The mean line segment length l^_ is the average length of a line segment in line segment picking within some given shape. As summarized in the following table (where Delta(3) ...

Any real function u(x,y) with continuous second partial derivatives which satisfies Laplace's equation, del ^2u(x,y)=0, (1) is called a harmonic function. Harmonic functions ...

A spherical harmonic of the form sin(mphi)P_m^m(costheta) or cos(mphi)P_m^m(costheta).