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An even Walsh function with sequency k defined by Cal(n,k)=W(n,2k+1).

An odd Walsh function with sequency k defined by Sal(n,k)=W(n,2k).

A function whose value decreases more quickly than any polynomial is said to be an exponentially decreasing function. The prototypical example is the function e^(-x), plotted ...

A function whose value increases more quickly than any polynomial is said to be an exponentially increasing function. The prototypical example is the function e^x, plotted ...

A function whose value decreases to zero more slowly than any nonzero polynomial is said to be a logarithmically decreasing function. The prototypical example is the function ...

A function whose value increases more slowly to infinity than any nonconstant polynomial is said to be a logarithmically increasing function. The prototypical example is the ...

A function f(x) decreases on an interval I if f(b)<=f(a) for all b>a, where a,b in I. If f(b)<f(a) for all b>a, the function is said to be strictly decreasing. Conversely, a ...

A function f(x) increases on an interval I if f(b)>=f(a) for all b>a, where a,b in I. If f(b)>f(a) for all b>a, the function is said to be strictly increasing. Conversely, a ...

A function S_n(z) which satisfies the recurrence relation S_(n-1)(z)-S_(n+1)(z)=2S_n^'(z) together with S_1(z)=-S_0^'(z) is called a hemicylindrical function.

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...