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There exist numbers y_1<y_2<...<y_(n-1), a<y_(n-1), y_(n-1)<b, such that lambda_nu=alpha(y_nu)-alpha(y_(nu-1)), (1) where nu=1, 2, ..., n, y_0=a and y_n=b. Furthermore, the ...

An algebraic surface of degree 7. The Labs septic is an example of a septic surface.

The bias of a series is defined as Q[a_i,a_(i+1),a_(i+2)]=(a_ia_(i+2)-a_(i+1)^2)/(a_ia_(i+1)a_(i+2)). A series is geometric iff Q=0. A series is artistic iff the bias is ...

If f(x)=f_0+f_1x+f_2x^2+...+f_nx^n+..., (1) then S(n,j)=f_jx^j+f_(j+n)x^(j+n)+f_(j+2n)x^(j+2n)+... (2) is given by S(n,j)=1/nsum_(t=0)^(n-1)w^(-jt)f(w^tx), (3) where ...

A set is a finite or infinite collection of objects in which order has no significance, and multiplicity is generally also ignored (unlike a list or multiset). Members of a ...

One of the disjoint subsets making up a set partition. A block containing n elements is called an n-block. The partitioning of sets into blocks can be denoted using a ...

An algebraic curve of degree six. Examples include the astroid, atriphtaloid, Cayley's sextic, cornoid, cycloid of Ceva, dumbbell curve, ellipse evolute, epicycloid, Freeth's ...

If a triangle is inscribed in a conic section, any line conjugate to one side meets the other two sides in conjugate points.

Although a numerically computed chaotic trajectory diverges exponentially from the true trajectory with the same initial coordinates, there exists an errorless trajectory ...

A generalization of the Bessel differential equation for functions of order 0, given by zy^('')+y^'+(z+A)y=0. Solutions are y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz), where ...