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A continuous homomorphism of a group into the nonzero complex numbers. A multiplicative character omega gives a group representation on the one-dimensional space C of complex ...

A function f(m) is called multiplicative if (m,m^')=1 (i.e., the statement that m and m^' are relatively prime) implies f(mm^')=f(m)f(m^') (Wilf 1994, p. 58). Examples of ...

The natural domain of a function is the maximal chain of domains on which it can be analytically continued to a single-valued function.

Let f:R->R, then the negative part of f is the function f^-:R->R defined by f^-(x)=max(-f(x),0). Note that the negative part is itself a nonnegative function. The negative ...

The negative real axis is the portion of the real axis with x<0.

A composition of a function f degreesf with itself gives a nested function f(f(x)), f degreesf degreesf which gives f(f(f(x)), etc. Function nesting is implemented in the ...

A pile of counters in a game of nim. The nim-heap illustrated above corresponds to the game of Marienbad.

A positive value of n for which x-phi(x)=n has no solution, where phi(x) is the totient function. The first few are 10, 26, 34, 50, 52, ... (OEIS A005278).

A positive even value of n for which phi(x)=n, where phi(x) is the totient function, has no solution. The first few are 14, 26, 34, 38, 50, ... (OEIS A005277).

Two functions f(x) and g(x) are orthogonal over the interval a<=x<=b with weighting function w(x) if <f(x)|g(x)>=int_a^bf(x)g(x)w(x)dx=0. (1) If, in addition, ...