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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 ...

A function for which several distinct functional values correspond (as a result of different continuations) to one and the same point (Knopp 1996, p. 94).

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 negative number multiplied by another negative number gives a positive number.

For a set of positive gamma_k, k=0, 1, 2..., Turán's inequalities are given by gamma_k^2-gamma_(k-1)gamma_(k+1)>=0 for k=1, 2, ....

The limit of an upper sum, when it exists, as the mesh size approaches 0.

For a given bounded function f(x) over a partition of a given interval, the upper sum is the sum of box areas M^*Deltax_k using the supremum M of the function f(x) in each ...