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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) ...

If f(x) is positive and decreases to 0, then an Euler constant gamma_f=lim_(n->infty)[sum_(k=1)^nf(k)-int_1^nf(x)dx] can be defined. For example, if f(x)=1/x, then ...

An Euler-Jacobi pseudoprime to a base a is an odd composite number n such that (a,n)=1 and the Jacobi symbol (a/n) satisfies (a/n)=a^((n-1)/2) (mod n) (Guy 1994; but note ...

There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...

The Euler triangle of a triangle DeltaABC is the triangle DeltaE_AE_BE_C whose vertices are the midpoints of the segments joining the orthocenter H with the respective ...

Ein(z) = int_0^z((1-e^(-t))dt)/t (1) = E_1(z)+lnz+gamma, (2) where gamma is the Euler-Mascheroni constant and E_1 is the En-function with n=1.

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

An Euler brick is a cuboid that possesses integer edges a>b>c and face diagonals d_(ab) = sqrt(a^2+b^2) (1) d_(ac) = sqrt(a^2+c^2) (2) d_(bc) = sqrt(b^2+c^2). (3) If the ...

The Euler infinity point is the intersection of the Euler line and line at infinity. Since it lies on the line at infinity, it is a point at infinity. It has triangle center ...

The four parameters e_0, e_1, e_2, and e_3 describing a finite rotation about an arbitrary axis. The Euler parameters are defined by e_0 = cos(phi/2) (1) e = [e_1; e_2; e_3] ...