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Let f(x) be a real entire function of the form f(x)=sum_(k=0)^inftygamma_k(x^k)/(k!), (1) where the gamma_ks are positive and satisfy Turán's inequalities ...

The limit of a lower sum, when it exists, as the mesh size approaches 0.

For a given function f(x) over a partition of a given interval, the lower sum is the sum of box areas m^*Deltax_k using the infimum m of the function f(x) in each subinterval ...

When a closed interval [a,b] is partitioned by points a<x_1<x_2<...<x_(n-1)<b, the lengths of the resulting intervals between the points are denoted Deltax_1, Deltax_2, ..., ...

A technically defined group characterizing a system of linear differential equations y_j^'=sum_(k=1)^na_(jk)(x)y_k for j=1, ..., n, where a_(jk) are complex analytic ...

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

The set of prime numbers, sometimes denoted P (Derbyshire 2004, p. 163), and implemented in the Wolfram Language as Primes. In the Wolfram Language, a quantity can be tested ...

A proper factor of a positive integer n is a factor of n other than 1 or n (Derbyshire 2004, p. 32). For example, 2 and 3 are positive proper factors of 6, but 1 and 6 are ...

A proper fraction is a fraction p/q with p,q>0 such that p/q<1. A fraction p/q>1 is called an improper fraction.

A removable singularity is a singular point z_0 of a function f(z) for which it is possible to assign a complex number in such a way that f(z) becomes analytic. A more ...