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Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

For homogeneous polynomials P and Q of degree n, [P,Q]=sum_(i_1,...,i_n>=0)(i_1!...i_n!)(a_(i,...,i_n)b_(i_1,...,i_n)).

An operator Gamma=sum_(i=1)^me_i^Ru^(iR) on a representation R of a Lie algebra.

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

For a finite group of h elements with an n_ith dimensional ith irreducible representation, sum_(i)n_i^2=h.

Given a hypergeometric series sum_(k)c_k, c_k is called a hypergeometric term (Koepf 1998, p. 12).

Given a function of the form y=Ax^B, (1) least squares fitting gives the coefficients as b = ...

The inverse transform sum_(n=1)^infty(a_nx^n)/(n!)=ln(1+sum_(n=1)^infty(b_nx^n)/(n!)) of the exponential transform ...

A nonuniform rational B-spline surface of degree (p,q) is defined by ...

Approximates the possible values of y in terms of x if sum_(i,j=0)^na_(ij)x^iy^j=0.