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The Lehmer-Mahler is the following integral representation for the Legendre polynomial P_n(x): P_n(costheta) = 1/piint_0^pi(costheta+isinthetacosphi)^ndphi (1) = ...

Let S be a nonempty set of real numbers that has an upper bound. Then a number c is called the least upper bound (or the supremum, denoted supS) for S iff it satisfies the ...

A nonnegative measurable function f is called Lebesgue integrable if its Lebesgue integral intfdmu is finite. An arbitrary measurable function is integrable if f^+ and f^- ...

In calculus, geometry, and plotting contexts, the term "linear function" means a function whose graph is a straight line, i.e., a polynomial function of degree 0 or 1. A ...

A lozenge (or rhombus) algorithm is a class of transformation that can be used to attempt to produce series convergence improvement (Hamming 1986, p. 207). The best-known ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

A multivariate is a vector each of whose elements is a variate. The variates need not be independent, and if they are not, a correlation is said to exist between them. The ...

The nested radical constant is the constant defined by C = sqrt(1+sqrt(2+sqrt(3+sqrt(4+sqrt(5+...))))) (1) = 1.75793275... (2) (OEIS A072449). No closed-form expression is ...

An operator A:f^((n))(I)|->f(I) assigns to every function f in f^((n))(I) a function A(f) in f(I). It is therefore a mapping between two function spaces. If the range is on ...