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rho_n(nu,x)=((1+nu-n)_n)/(sqrt(n!x^n))_1F_1(-n;1+nu-n;x), where (a)_n is a Pochhammer symbol and _1F_1(a;b;z) is a confluent hypergeometric function of the first kind.

Every bounded operator T acting on a Hilbert space H has a decomposition T=U|T|, where |T|=(T^*T)^(1/2) and U is a partial isometry. This decomposition is called polar ...

The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

The polynomial giving the number of colorings with m colors of a structure defined by a permutation group.

One of the symmetry groups of the Platonic solids. There are three polyhedral groups: the tetrahedral group of order 12, the octahedral group of order 24, and the icosahedral ...

The ith Pontryagin class of a vector bundle is (-1)^i times the ith Chern class of the complexification of the vector bundle. It is also in the 4ith cohomology group of the ...

Let A be a C^*-algebra, then a linear functional f on A is said to be positive if it is a positive map, that is f(a)>=0 for all a in A_+. Every positive linear functional is ...

You buy 100 pounds of potatoes and are told that they are 99% water. After leaving them outside, you discover that they are now 98% water. The weight of the dehydrated ...

The algebra A is called a pre-C^*-algebra if it satisfies all conditions to be a C^*-algebra except that its norm need not be complete.

The problem of forecasting future values X_(t+tau) (tau>0) of a weakly stationary process {X_t} from the known values X_s (s<=t).