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Define I_n=(-1)^nint_0^infty(lnz)^ne^(-z)dz, (1) then I_n=(-1)^nGamma^((n))(1), (2) where Gamma^((n))(z) is the nth derivative of the gamma function. Particular values ...

A function on the reals R is a step function if it can be written as a finite linear combination of semi-open intervals [a,b) subset= R. Therefore, a step function f can be ...

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

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.

The name Lobachevsky's function is sometimes given to the function Lambda(theta)=1/2Cl_2(2theta), also denoted Pi(theta), where Cl_2(x) is Clausen's integral.

A function for which all critical points are nondegenerate and all critical levels are different.

A function f defined on a subset S subset R^n is said to be pseudoconcave if -f is pseudoconvex.

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

A simple function is a finite sum sum_(i)a_ichi_(A_i), where the functions chi_(A_i) are characteristic functions on a set A. Another description of a simple function is a ...

By analogy with the sinc function, define the tanc function by tanc(z)={(tanz)/z for z!=0; 1 for z=0. (1) Since tanz/z is not a cardinal function, the "analogy" with the sinc ...