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A real function is said to be differentiable at a point if its derivative exists at that point. The notion of differentiability can also be extended to complex functions ...

A multiplicative number theoretic function is a number theoretic function f that has the property f(mn)=f(m)f(n) (1) for all pairs of relatively prime positive integers m and ...

Minimal surfaces are defined as surfaces with zero mean curvature. A minimal surface parametrized as x=(u,v,h(u,v)) therefore satisfies Lagrange's equation, ...

The gamma product (e.g., Prudnikov et al. 1986, pp. 22 and 792), is defined by Gamma[a_1,...,a_m; b_1,...,b_n]=(Gamma(a_1)...Gamma(a_m))/(Gamma(b_1)...Gamma(b_n)), where ...

J_n(z) = 1/(2pi)int_(-pi)^pie^(izcost)e^(in(t-pi/2))dt (1) = (i^(-n))/piint_0^pie^(izcost)cos(nt)dt (2) = 1/piint_0^picos(zsint-nt)dt (3) for n=0, 1, 2, ..., where J_n(z) is ...

The symbol defined by c^(a/b) = c(c+b)(c+2b)...[c+(a-1)b] (1) = b^a(c/b)_a (2) = (b^aGamma(a+c/b))/(Gamma(c/b)), (3) where (a)_n is the Pochhammer symbol and Gamma(z) is the ...

A function f(x) is logarithmically convex on the interval [a,b] if f>0 and lnf(x) is convex on [a,b]. If f(x) and g(x) are logarithmically convex on the interval [a,b], then ...

A piecewise linear function is a function composed of some number of linear segments defined over an equal number of intervals, usually of equal size. For example, consider ...

A generalization of the polylogarithm function defined by S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt. The function reduces to the usual ...

If f:D->Y is a map (a.k.a. function, transformation, etc.) over a domain D, then the image of f, also called the range of D under f, is defined as the set of all values that ...