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Let T(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Define f_m(x)=product_(t in T(m))(x-t). (1) Then a ...

If f(x) is piecewise continuous and has a generalized Fourier series sum_(i)a_iphi_i(x) (1) with weighting function w(x), it must be true that ...

The "binary" Champernowne constant is obtained by concatenating the binary representations of the integers C_2 = 0.(1)(10)(11)(100)(101)(110)(111)..._2 (1) = ...

The binary logarithm log_2x is the logarithm to base 2. The notation lgx is sometimes used to denote this function in number theoretic literature. However, because Russian ...

Bisection is the division of a given curve, figure, or interval into two equal parts (halves). A simple bisection procedure for iteratively converging on a solution which is ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_5=f(x_5). Then Boole's rule approximating the ...

Various forms of opening and closing bracket-like delimiters are used for a number of distinct notational purposes in mathematics. The most common variants of bracket ...

For any sets A and B, their cardinal numbers satisfy |A|<=|B| iff there is a one-to-one function f from A into B (Rubin 1967, p. 266; Suppes 1972, pp. 94 and 116). It is easy ...

In general, the pedal curve of the cardioid is a slightly complicated function. The pedal curve of the cardioid with respect to the center of its conchoidal circle is the ...

The central difference for a function tabulated at equal intervals f_n is defined by delta(f_n)=delta_n=delta_n^1=f_(n+1/2)-f_(n-1/2). (1) First and higher order central ...