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The second solution Q_l(x) to the Legendre differential equation. The Legendre functions of the second kind satisfy the same recurrence relation as the Legendre polynomials. ...

Consider the sequence of partial sums defined by s_n=sum_(k=1)^n(-1)^kk^(1/k). (1) As can be seen in the plot above, the sequence has two limit points at -0.812140... and ...

Matrix diagonalization is the process of taking a square matrix and converting it into a special type of matrix--a so-called diagonal matrix--that shares the same fundamental ...

The power series that defines the exponential map e^x also defines a map between matrices. In particular, exp(A) = e^(A) (1) = sum_(n=0)^(infty)(A^n)/(n!) (2) = ...

If r is an algebraic number of degree n, then the totality of all expressions that can be constructed from r by repeated additions, subtractions, multiplications, and ...

A system of curvilinear coordinates in which two sets of coordinate surfaces are obtained by revolving the curves of the elliptic cylindrical coordinates about the y-axis ...

The osculating circle of a curve C at a given point P is the circle that has the same tangent as C at point P as well as the same curvature. Just as the tangent line is the ...

The pedal curve of the parabola with parametric equations x = at^2 (1) y = 2at (2) with pedal point (x_0,y_0) is x_p = ((x_0-a)t^2+y_0t)/(t^2+1) (3) y_p = ...

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

Two planes always intersect in a line as long as they are not parallel. Let the planes be specified in Hessian normal form, then the line of intersection must be ...