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A system of curvilinear coordinates variously denoted (xi,eta,phi) (Arfken 1970) or (theta,eta,psi) (Moon and Spencer 1988). Using the notation of Arfken, the bispherical ...

One of the polynomials obtained by taking powers of the Brahmagupta matrix. They satisfy the recurrence relation x_(n+1) = xx_n+tyy_n (1) y_(n+1) = xy_n+yx_n. (2) A list of ...

A centered polygonal number consisting of a central dot with five dots around it, and then additional dots in the gaps between adjacent dots. The general term is ...

In the figure above with tangent line PT and secant line PA, (PA)/(PT)=(PT)/(PB) (1) (Jurgensen et al. 1963, p. 346). The line tangent to a circle of radius a centered at ...

A cubic triangular number is a positive integer that is simultaneously cubic and triangular. Such a number must therefore satisfy T_n=m^3 for some positive integers n and m, ...

The first Debye function is defined by D_n^((1))(x) = int_0^x(t^ndt)/(e^t-1) (1) = x^n[1/n-x/(2(n+1))+sum_(k=1)^(infty)(B_(2k)x^(2k))/((2k+n)(2k!))], (2) for |x|<2pi, n>=1, ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

Let 0<k^2<1. The incomplete elliptic integral of the third kind is then defined as Pi(n;phi,k) = int_0^phi(dtheta)/((1-nsin^2theta)sqrt(1-k^2sin^2theta)) (1) = ...

The pedal curve of an epicycloid x = (a+b)cost-b[((a+b)t)/b] (1) y = (a+b)sint-bsin[((a+b)t)/b] (2) with pedal point at the origin is x_p = 1/2(a+2b){cost-cos[((a+b)t)/b]} ...

The general nonhomogeneous differential equation is given by x^2(d^2y)/(dx^2)+alphax(dy)/(dx)+betay=S(x), (1) and the homogeneous equation is x^2y^('')+alphaxy^'+betay=0 (2) ...