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The inverse of a square matrix A, sometimes called a reciprocal matrix, is a matrix A^(-1) such that AA^(-1)=I, (1) where I is the identity matrix. Courant and Hilbert (1989, ...

The modern definition of the q-hypergeometric function is _rphi_s[alpha_1,alpha_2,...,alpha_r; beta_1,...,beta_s;q,z] ...

Angle trisection is the division of an arbitrary angle into three equal angles. It was one of the three geometric problems of antiquity for which solutions using only compass ...

Watson (1939) considered the following three triple integrals, I_1 = 1/(pi^3)int_0^piint_0^piint_0^pi(dudvdw)/(1-cosucosvcosw) (1) = (4[K(1/2sqrt(2))]^2)/(pi^2) (2) = ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

The pure equation x^p=C of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field. Jeffreys and Jeffreys ...

A factorization of the form 2^(4n+2)+1=(2^(2n+1)-2^(n+1)+1)(2^(2n+1)+2^(n+1)+1). (1) The factorization for n=14 was discovered by Aurifeuille, and the general form was ...

There are several meanings of the word content in mathematics. The content of a polytope or other n-dimensional object is its generalized volume (i.e., its "hypervolume"). ...

A test to determine if a given series converges or diverges.

A point traced out twice as a closed curve is traversed. The maximum number of double points for a nondegenerate quartic curve is three. An ordinary double point is also ...