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A Lambert series is a series of the form F(x)=sum_(n=1)^inftya_n(x^n)/(1-x^n) (1) for |x|<1. Then F(x) = sum_(n=1)^(infty)a_nsum_(m=1)^(infty)x^(mn) (2) = ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

Liouville's constant, sometimes also called Liouville's number, is the real number defined by L=sum_(n=1)^infty10^(-n!)=0.110001000000000000000001... (OEIS A012245). ...

Let f(z) be an entire function such that f(n) is an integer for each positive integer n. Then Pólya (1915) showed that if lim sup_(r->infty)(lnM_r)/r<ln2=0.693... (1) (OEIS ...

By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

An ordered factorization is a factorization (not necessarily into prime factors) in which a×b is considered distinct from b×a. The following table lists the ordered ...

Circumscribe a triangle about a circle, another circle around the triangle, a square outside the circle, another circle outside the square, and so on. The circumradius and ...

A rational number is a number that can be expressed as a fraction p/q where p and q are integers and q!=0. A rational number p/q is said to have numerator p and denominator ...

Let N steps of equal length be taken along a line. Let p be the probability of taking a step to the right, q the probability of taking a step to the left, n_1 the number of ...