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sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...

Let {p_n(x)} be orthogonal polynomials associated with the distribution dalpha(x) on the interval [a,b]. Also let rho=c(x-x_1)(x-x_2)...(x-x_l) (for c!=0) be a polynomial of ...

Chrystal's identity is the algebraic identity ((b-c)^2+(b+c)^2+2(b^2-c^2))/((b^4-2b^2c^2+c^4)[1/((b-c)^2)+2/(b^2-c^2)+1/((b+c)^2)])=1 given as an exercise by Chrystal (1886).

A class number formula is a finite series giving exactly the class number of a ring. For a ring of quadratic integers, the class number is denoted h(d), where d is the ...

Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...

The four following types of groups, 1. linear groups, 2. orthogonal groups, 3. symplectic groups, and 4. unitary groups, which were studied before more exotic types of groups ...

The dimension of a special series can never exceed half its order.

A subset of a topological group which is closed as a subset and also a subgroup.

A multiplicative factor (usually indexed) such as one of the constants a_i in the polynomial a_nx^n+a_(n-1)x^(n-1)+...+a_2x^2+a_1x+a_0. In this polynomial, the monomials are ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.