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|_n]!={n! for n>=0; ((-1)^(-n-1))/((-n-1)!) for n<0. (1) The Roman factorial arises in the definition of the harmonic logarithm and Roman coefficient. It obeys the identities ...

Let E be a Euclidean space, (beta,alpha) be the dot product, and denote the reflection in the hyperplane P_alpha={beta in E|(beta,alpha)=0} by ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then the Selberg zeta function is defined as ...

A spheroid is an ellipsoid having two axes of equal length, making it a surface of revolution. By convention, the two distinct axis lengths are denoted a and c, and the ...

Let a_1=1 and define a_(n+1) to be the least integer greater than a_n which cannot be written as the sum of at most h>=2 addends among the terms a_1, a_2, ..., a_n. This ...

Let V be a real vector space (e.g., the real continuous functions C(I) on a closed interval I, two-dimensional Euclidean space R^2, the twice differentiable real functions ...

Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

(Bailey 1935, p. 25), where _7F_6(a_1,...,a_7;b_1,...,b_6) and _4F_3(a_1,...,a_4;b_1,b_2,b_3) are generalized hypergeometric functions with argument z=1 and Gamma(z) is the ...

The constants C_n defined by C_n=[int_0^infty|d/(dt)((sint)/t)^n|dt]-1. (1) These constants can also be written as the sums C_n=2sum_(k=1)^infty(1+x_k^2)^(-n/2), (2) and ...

A 4-cusped hypocycloid which is sometimes also called a tetracuspid, cubocycloid, or paracycle. The parametric equations of the astroid can be obtained by plugging in n=a/b=4 ...