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

Find the tunnel between two points A and B on a gravitating sphere which gives the shortest transit time under the force of gravity. Assume the sphere to be nonrotating, of ...

A fixed point for which the stability matrix has one zero eigenvector with negative eigenvalue lambda<0.

A point x_0 at which the derivative of a function f(x) vanishes, f^'(x_0)=0. A stationary point may be a minimum, maximum, or inflection point.

The second-order ordinary differential equation y^('')-[(M^2-1/4+K^2-2MKcosx)/(sin^2x)+(sigma+K^2+1/4)]y=0.

By analogy with the tanc function, define the tanhc function by tanhc(z)={(tanhz)/z for z!=0; 1 for z=0. (1) It has derivative (dtanhc(z))/(dz)=(sech^2z)/z-(tanhz)/(z^2). (2) ...

The trivial group, denoted E or <e>, sometimes also called the identity group, is the unique (up to isomorphism) group containing exactly one element e, the identity element. ...

The function defined by U(n)=(n!)^(n!). The values for n=0, 1, ..., are 1, 1, 4, 46656, 1333735776850284124449081472843776, ... (OEIS A046882).

Variables x_i and x_j are said to be uncorrelated if their covariance is zero: cov(x_i,x_j)=0. Independent statistics are always uncorrelated, but the converse is not ...

A fixed point for which the stability matrix has eigenvalues of the form lambda_+/-=alpha+/-ibeta (with alpha,beta>0).