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Trigonometry

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

A statement letter or a negation of a statement letter (Mendelson 1997, p. 30).

A prime gap of length n is a run of n-1 consecutive composite numbers between two successive primes. Therefore, the difference between two successive primes p_k and p_(k+1) ...

A group homomorphism is a map f:G->H between two groups such that the group operation is preserved:f(g_1g_2)=f(g_1)f(g_2) for all g_1,g_2 in G, where the product on the ...

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) = (r^.)/(|r^.|) (1) = (r^.)/(s^.) (2) = (dr)/(ds), (3) where t is a parameterization ...

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...

The number of data points which fall within a given class in a frequency distribution.

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 ...