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The Laguerre polynomials are solutions L_n(x) to the Laguerre differential equation with nu=0. They are illustrated above for x in [0,1] and n=1, 2, ..., 5, and implemented ...

The p-layer of H, L_(p^')(H) is the unique minimal normal subgroup of H which maps onto E(H/O_(p^')(H)).

The incenter I is the center of the incircle for a polygon or insphere for a polyhedron (when they exist). The corresponding radius of the incircle or insphere is known as ...

In this work, the name Pythagoras's constant will be given to the square root of 2, sqrt(2)=1.4142135623... (1) (OEIS A002193), which the Pythagoreans proved to be ...

Not decidable as a result of being neither formally provable nor unprovable.

Schmidt (1993) proposed the problem of determining if for any integer r>=2, the sequence of numbers {c_k^((r))}_(k=1)^infty defined by the binomial sums sum_(k=0)^n(n; ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

Given a simplex of unit content in Euclidean d-space, pick n>=d+1 points uniformly and independently at random, and denote the expected content of their convex hull by ...

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

alpha_n(z) = int_1^inftyt^ne^(-zt)dt (1) = n!z^(-(n+1))e^(-z)sum_(k=0)^(n)(z^k)/(k!). (2) It is equivalent to alpha_n(z)=E_(-n)(z), (3) where E_n(z) is the En-function.