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A covariant tensor, denoted with a lowered index (e.g., a_mu) is a tensor having specific transformation properties. In general, these transformation properties differ from ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...

There are a couple of versions of this theorem. Basically, it says that any bounded linear functional T on the space of compactly supported continuous functions on X is the ...

The square torus is the quotient of the plane by the integer lattice.

Taylor's theorem states that any function satisfying certain conditions may be represented by a Taylor series, Taylor's theorem (without the remainder term) was devised by ...

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Analysis

Calculating the 13th root of a large number (that is a perfect 13th power) is a famous mental calculation challenge. However, because of difficulties in standardizing the ...

Let x_0 be a rational number in the closed interval [0,1], and generate a sequence using the map x_(n+1)=2x_n (mod 1). (1) Then the number of periodic map orbits of period p ...

The Abel-Plana formula gives an expression for the difference between a discrete sum and the corresponding integral. The formula can be derived from the argument principle ...