on an interval

SearchAdvancedHelp

(0.002 seconds)

1—10 of 142 matching pages

1: 1.4 Calculus of One Variable

… ►If $f(x_1)\le f(x_2)$ for every pair $x_1$, $x_2$ in an interval $I$ such that , then $f(x)$ is nondecreasing on $I$. … ► … ►If $f(x)$ is continuous on an interval $I$ save for a finite number of simple discontinuities, then $f(x)$ is piecewise (or sectionally) continuous on $I$. … ►If $f^{(n)}$ exists and is continuous on an interval $I$, then we write $f\in C^n(I)$. … ►For $\alpha (x)$ nondecreasing on the closure $I$ of an interval $(a,b)$, the measure $d\alpha$ is absolutely continuous if $\alpha (x)$ is continuous and there exists a weight function $w(x)\ge 0$, Riemann (or Lebesgue) integrable on finite subintervals of $I$, such that …

2: Bibliography Z

… ►

On some classes of polynomials orthogonal on arcs of the unit circle connected with symmetric orthogonal polynomials on an interval. J. Approx. Theory 94 (1), pp. 73–106.

ⓘ

External Links:

ISSN 0021-9045, Link, MathReview (T. S. Chihara), ZentralBlatt

Referenced by:

§18.33(iii).

Encodings:

BibTeX

…

3: 26.2 Basic Definitions

… ►Unless otherwise specified, it consists of horizontal segments corresponding to the vector $(1,0)$ and vertical segments corresponding to the vector $(0,1)$. For an example see Figure 26.9.2. … ►A partition of a set $S$ is an unordered collection of pairwise disjoint nonempty sets whose union is $S$. … ►A partition of a nonnegative integer $n$ is an unordered collection of positive integers whose sum is $n$. As an example, $\{1,1,1,2,4,4\}$ is a partition of 13. …

4: 28.17 Stability as $x\to \pm \mathrm{\infty }$

… ►However, if $\mathrm{\Im }\nu \ne 0$, then $(a,q)$ always comprises an unstable pair. …

5: 18.40 Methods of Computation

… ►

►►

Figure 18.40.1: Histogram approximations to the Repulsive Coulomb–Pollaczek, RCP, weight function integrated over $[-1,x)$, see Figure 18.39.2 for an exact result, for $Z=+1$, shown for $N=12$ and $N=120$. Magnify

… ►Here $x(t,N)$ is an interpolation of the abscissas $x_{i,N},i=1,2,\mathrm{\dots },N$, that is, $x(i,N)=x_{i,N}$, allowing differentiation by $i$. … ►This is a challenging case as the desired $w^{\mathrm{RCP}}(x)$ on $[-1,1]$ has an essential singularity at $x=-1$. …

6: Bibliography K

… ►

Algorithm 763: INTERVAL_ARITHMETIC: A Fortran 90 module for an interval data type. ACM Trans. Math. Software 22 (4), pp. 385–392.

ⓘ

External Links:

ISSN 0098-3500, Document, GAMS (module 763; package TOMS), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

…

7: 10.23 Sums

… ►provided that $f(t)$ is of bounded variation (§1.4(v)) on an interval $[a,b]$ with . …

8: 1.6 Vectors and Vector-Valued Functions

… ►A path is defined by $𝐜(t)=(x(t),y(t),z(t))$, with $t$ ranging over an interval and $x(t),y(t),z(t)$ differentiable. … ►with $(u,v)\in D$, an open set in the plane. …

9: 2.3 Integrals of a Real Variable

… ► $k$ ($\le \mathrm{\infty }$) and $\lambda$ are positive constants, $\alpha$ is a variable parameter in an interval ${\alpha }_1\le \alpha \le {\alpha }_2$ with ${\alpha }_1\le 0$ and , and $x$ is a large positive parameter. …

10: 18.1 Notation

… ► ►►►

$x,y,t$	real variables.
…
$w(x)$	weight function $(\ge 0)$ on an open interval $(a,b)$.
…

…