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The symmetric group S_n of degree n is the group of all permutations on n symbols. S_n is therefore a permutation group of order n! and contains as subgroups every group of ...

The hyperbolic sine is defined as sinhz=1/2(e^z-e^(-z)). (1) The notation shz is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram ...

A division algebra, also called a "division ring" or "skew field," is a ring in which every nonzero element has a multiplicative inverse, but multiplication is not ...

The study of angles and of the angular relationships of planar and three-dimensional figures is known as trigonometry. The trigonometric functions (also called the circular ...

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

The Ree group R(q) is the automorphism group of a S(2,q+1,q^3+1) Steiner system.

Let p_i denote the ith prime, and write m=product_(i)p_i^(v_i). Then the exponent vector is v(m)=(v_1,v_2,...).

The primes with Legendre symbol (n/p)=1 (less than N=pi(d) for trial divisor d) which need be considered when using the quadratic sieve factorization method.

A primitive subgroup of the symmetric group S_n is equal to either the alternating group A_n or S_n whenever it contains at least one permutation which is a q-cycle for some ...

In the depiction of a row of identical columns parallel to the plane of a perspective drawing, the outer columns should appear wider even though they are farther away.