May 17, 2012 · In Elias Stein's Real Analysis, at the beginning of Chapter 4.1, it reads "We shall say that $f$ is finite-valued if $-\infty<f (x)<\infty$ for all $x$." A function is finite if it never …

A holonomic function or sequence can be represented by a finite amount of data, namely an annihilating operator and a finite set of initial values, and the closure properties allow carrying …

This book is a comprehensive introduction to the theory of D-finite functions with a special emphasis on computer algebra algorithms.

If the argument is infinite or not a defined number (NaN), the FINITE function returns 0 (False). The result is a byte expression of the same structure as the argument X.

This textbook was compiled as an Open Educational Resource for the University of St. Thomas (St. Paul, MN) MATH 101 "Finite Mathematics" course. The course covers topics in set theory, …

Oct 26, 2022 · The isfinite macro and the _finite and _finitef functions return a non-zero value if x is either a normal or subnormal finite value. They return 0 if the argument is infinite or a NaN. …

Some real analysis texts allow functions to take the value $\infty$. So something like $f (x) = x$ is finite but not bounded, while, say, $f (x) = \frac {1} {\lvert x \rvert}$ for nonzero $x$ and $f (0) = …

If the domain of a function is finite, then the function can be completely specified in this way. For example, the multiplication function defined as can be represented by the familiar …

In good cases, functions with compact support are dense in the space of functions that vanish at infinity, but this property requires some technical work to justify in a given example.

In mathematical analysis, a function of bounded variation, also known as BV function, is a real -valued function whose total variation is bounded (finite): the graph of a function having this …