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A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

A fractal process for which H<1/2, so r<0.

For 0<=x<=pi/2, 2/pix<=sinx<=x.

A fractal process for which H>1/2, so r>0.

f(z)=k/((cz+d)^r)f((az+b)/(cz+d)) where I[z]>0.

An equation of the form P(x)=0, where P(x) is a polynomial.

If a polynomial P(x) has a root x=a, i.e., if P(a)=0, then x-a is a factor of P(x).

A quadratic field Q(sqrt(D)) with D>0.

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) ...

A generalized Moore graph is a regular graph of degree r where the counts of vertices at each distance d=0, 1, ... from any vertex are 1, r, r(r-1), r(r-1)^2, r(r-1)^3, ..., ...