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There are three types of so-called fundamental forms. The most important are the first and second (since the third can be expressed in terms of these). The fundamental forms ...

Stratton (1935), Chu and Stratton (1941), and Rhodes (1970) define the spheroidal functions as those solutions of the differential equation (1) that remain finite at the ...

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

A stack is a data structure which is a special kind of list in which elements may be added to or removed from the top only. These actions are called a push or a pop, ...

Chebyshev-Gauss quadrature, also called Chebyshev quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function W(x)=(1-x^2)^(-1/2) (Abramowitz and ...

An algebraic surface with affine equation P_d(x_1,x_2)+T_d(x_3)=0, (1) where T_d(x) is a Chebyshev polynomial of the first kind and P_d(x_1,x_2) is a polynomial defined by ...

A Fourier series-like expansion of a twice continuously differentiable function f(x)=1/2a_0+sum_(n=1)^inftya_nJ_0(nx) (1) for 0<x<pi, where J_0(x) is a zeroth order Bessel ...

A hypotrochoid is a roulette traced by a point P attached to a circle of radius b rolling around the inside of a fixed circle of radius a, where P is a distance h from the ...

The limaçon trisectrix is a trisectrix that is a special case of the rose curve with n=1/3 (possibly with translation, rotation, and scaling). It was studied by Archimedes, ...

The term perimeter refers either to the curve constituting the boundary of a lamina or else to the length of this boundary. The perimeter of a circle is called the ...