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The mean square deviation of the best local fit straight line to a staircase cumulative spectral density over a normalized energy scale.

Let H be a Hilbert space, B(H) the set of bounded linear operators from H to itself, T an operator on H, and sigma(T) the operator spectrum of T. Then if T in B(H) and T is ...

F(x) = -Li_2(-x) (1) = int_0^x(ln(1+t))/tdt, (2) where Li_2(x) is the dilogarithm.

F(x) = Li_2(1-x) (1) = int_(1-x)^0(ln(1-t))/tdt, (2) where Li_2(x) is the dilogarithm.

The sum of the absolute squares of the spherical harmonics Y_l^m(theta,phi) over all values of m is sum_(m=-l)^l|Y_l^m(theta,phi)|^2=(2l+1)/(4pi). (1) The double sum over m ...

A spheroidal harmonic is a special case of an ellipsoidal harmonic that satisfies the differential equation d/(dx)[(1-x^2)(dS)/(dx)]+(lambda-c^2x^2-(m^2)/(1-x^2))S=0 on the ...

A fixed point for which the eigenvalues are complex conjugates.

A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

A fixed point for which the stability matrix has equal negative eigenvalues.

A fixed point for which the stability matrix has both eigenvalues negative, so lambda_1<lambda_2<0.