Search Results for ""

The first example discovered of a map from a higher-dimensional sphere to a lower-dimensional sphere which is not null-homotopic. Its discovery was a shock to the ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

An operation on rings and modules. Given a commutative unit ring R, and a subset S of R, closed under multiplication, such that 1 in S, and 0 not in S, the localization of R ...

A formula which transforms a given coordinate system by rotating it through a counterclockwise angle Phi about an axis n^^. Referring to the above figure (Goldstein 1980), ...

erf(z) is the "error function" encountered in integrating the normal distribution (which is a normalized form of the Gaussian function). It is an entire function defined by ...

It is possible to perform multiplication of large numbers in (many) fewer operations than the usual brute-force technique of "long multiplication." As discovered by Karatsuba ...

The logarithm log_bx for a base b and a number x is defined to be the inverse function of taking b to the power x, i.e., b^x. Therefore, for any x and b, x=log_b(b^x), (1) or ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...

A figurate number of the form P_n^((4))=1/6n(n+1)(2n+1), (1) corresponding to a configuration of points which form a square pyramid, is called a square pyramidal number (or ...