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For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The plastic constant P, sometimes also called le nombre radiant, the minimal Pisot number, plastic number, plastic ratio, platin number, Siegel's number, or silver number, is ...

A polynomial A_n(x;a) given by the associated Sheffer sequence with f(t)=te^(at), (1) given by A_n(x;a)=x(x-an)^(n-1). (2) The generating function is ...

The Abel equation of the first kind is given by y^'=f_0(x)+f_1(x)y+f_2(x)y^2+f_3(x)y^3+... (Murphy 1960, p. 23; Zwillinger 1997, p. 120), and the Abel equation of the second ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

The nth order Bernstein expansion of a function f(x) in terms of a variable x is given by B_n(f,x)=sum_(j=0)^n(n; j)x^j(1-x)^(n-j)f(j/n), (1) (Gzyl and Palacios 1997, Mathé ...

The two recursive sequences U_n = mU_(n-1)+U_(n-2) (1) V_n = mV_(n-1)+V_(n-2) (2) with U_0=0, U_1=1 and V_0=2, V_1=m, can be solved for the individual U_n and V_n. They are ...

A sequence of polynomials p_n satisfying the identities p_n(x+y)=sum_(k>=0)(n; k)p_k(x)p_(n-k)(y).

A polynomial with 2 terms.

B(x,y)=[x y; +/-ty +/-x]. (1) It satisfies B(x_1,y_1)B(x_2,y_2)=B(x_1x_2+/-ty_1y_2,x_1y_2+/-y_1x_2). (2) Powers of the matrix are defined by B^n = [x y; ty x]^n (3) = [x_n ...