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There are several different definitions of conical coordinates defined by Morse and Feshbach (1953), Byerly (1959), Arfken (1970), and Moon and Spencer (1988). The ...

A conical wedge is an ungula obtained by cutting a solid cone with a plane placed at an angle oblique to its base. For the special conical wedge obtained from a cone of ...

A coordinate system composed of intersecting surfaces. If the intersections are all at right angles, then the curvilinear coordinates are said to form an orthogonal ...

The cylinder function is defined as C(x,y)={1 for sqrt(x^2+y^2)<=a; 0 for sqrt(x^2+y^2)>a. (1) The Bessel functions are sometimes also called cylinder functions. To find the ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...

Ellipsoidal harmonics of the second kind, also known as Lamé functions of the second kind, are variously defined as F_m^p(x)=(2m+1)E_m^p(x) ...

A variation of chess involving a change in the form of the board, the rules of play, or the pieces used. For example, the normal rules of chess can be used but with a ...

Poisson's equation is del ^2phi=4pirho, (1) where phi is often called a potential function and rho a density function, so the differential operator in this case is L^~=del ...

To solve the heat conduction equation on a two-dimensional disk of radius a=1, try to separate the equation using U(r,theta,t)=R(r)Theta(theta)T(t). (1) Writing the theta and ...

As shown by Morse and Feshbach (1953) and Arfken (1970), the Helmholtz differential equation is separable in oblate spheroidal coordinates.