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The definite integral int_a^bx^ndx={(b^(n+1)-a^(n+1))/(n+1) for n!=1; ln(b/a) for n=-1, (1) where a, b, and x are real numbers and lnx is the natural logarithm.

For any real alpha and beta such that beta>alpha, let p(alpha)!=0 and p(beta)!=0 be real polynomials of degree n, and v(x) denote the number of sign changes in the sequence ...

Schroeder (1991) calls the ceiling function symbols [ and ] the "gallows" because of their similarity in appearance to the structure used for hangings.

The point that inversion of a curve is performed with respect to.

The radius used in performing an inversion with respect to an inversion circle.

The repeated application of a transformation.

Given a function of the form y=a+blnx, (1) the coefficients can be found from least squares fitting as b = ...

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

The identities between the symmetric polynomials Pi_k(x_1,...,x_n) and the sums of kth powers of their variables S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k. (1) The identities are ...

The reciprocity theorem for x^8=q (mod p).