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Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by ...

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 ...

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

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^- ...

The Lebesgue measure is an extension of the classical notions of length and area to more complicated sets. Given an open set S=sum_(k)(a_k,b_k) containing disjoint intervals, ...

Each double point assigned to an irreducible algebraic curve whose curve genus is nonnegative imposes exactly one condition.

The term "left factorial" is sometimes used to refer to the subfactorial !n, the first few values for n=1, 2, ... are 1, 3, 9, 33, 153, 873, 5913, ... (OEIS A007489). ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

Given a map f:S->T between sets S and T, the map g:T->S is called a left inverse to f provided that g degreesf=id_S, that is, composing f with g from the left gives the ...

The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...