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The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

The sum-of-factorial powers function is defined by sf^p(n)=sum_(k=1)^nk!^p. (1) For p=1, sf^1(n) = sum_(k=1)^(n)k! (2) = (-e+Ei(1)+pii+E_(n+2)(-1)Gamma(n+2))/e (3) = ...

A general quartic surface defined by x^4+y^4+z^4+a(x^2+y^2+z^2)^2+b(x^2+y^2+z^2)+c=0 (1) (Gray 1997, p. 314). The above two images correspond to (a,b,c)=(0,0,-1), and ...

The quintuple product identity, also called the Watson quintuple product identity, states (1) It can also be written (2) or (3) The quintuple product identity can be written ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

A curve whose name means skull-like. It is given by the polar equation r=asint+bsqrt(1-pcos^2t)+csqrt(1-qcos^2t), where a,b,c>0, a<b+c, 0<p<1, 0<q<1, and p!=q. The top of the ...

The Gaussian integral, also called the probability integral and closely related to the erf function, is the integral of the one-dimensional Gaussian function over ...

The geometric distribution is a discrete distribution for n=0, 1, 2, ... having probability density function P(n) = p(1-p)^n (1) = pq^n, (2) where 0<p<1, q=1-p, and ...

Bracewell's term for the delta function.

Dawson's integral (Abramowitz and Stegun 1972, pp. 295 and 319), also sometimes called Dawson's function, is the entire function given by the integral F(x) = ...