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Pre-Calculus

A series suma(n)e^(-lambda(n)z), where a(n) and z are complex and {lambda(n)} is a monotonic increasing sequence of real numbers. The numbers lambda(n) are called the ...

Trigonometric functions of npi/7 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 7 is not a ...

Fatou dust is a Fatou set for a point outside the underlying set. Such a set has zero area and has an infinite number of disconnected components.

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

L_nu(z) = (1/2z)^(nu+1)sum_(k=0)^(infty)((1/2z)^(2k))/(Gamma(k+3/2)Gamma(k+nu+3/2)) (1) = (2(1/2z)^nu)/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)sinh(zcostheta)sin^(2nu)thetadtheta, ...

Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

An arithmetic function is a function f(n) defined for all n in N, usually taken to be complex-valued, so that f:N->C (Jones and Jones 1998, p. 143). An alternative definition ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...

Let (x_1,x_2) and (y_1,y_2) be two sets of complex numbers linearly independent over the rationals. Then the four exponential conjecture posits that at least one of ...