# range and domain

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## 8 matching pages

##### 1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

*range*$\mathcal{R}(T)=\{Tv\mid v\in \mathcal{D}(T)\}$. …

##### 2: 2.5 Mellin Transform Methods

##### 3: Bibliography G

##### 4: Bibliography F

##### 5: 2.8 Differential Equations with a Parameter

##### 6: 2.4 Contour Integrals

$z$ ranges along a ray or over an annular sector ${\theta}_{1}\le \theta \le {\theta}_{2}$, $|z|\ge Z$, where $\theta =\mathrm{ph}z$, $$, and $Z>0$. $I(z)$ converges at $b$ absolutely and uniformly with respect to $z$.

##### 7: 18.39 Applications in the Physical Sciences

*exceptional*, as opposed to

*regular*, zeros of the EOP’s, these latter belonging to the (real) orthogonality integration range. … ►Shizgal (2015, Chapter 2), contains a broad-ranged discussion of methods and applications for these, and other, non-classical weight functions. …

##### 8: Errata

In regard to the definition of the spherical
harmonics ${Y}_{l,m}$, the domain of the integer $m$ originally written
as $0\le m\le l$ has been replaced with the more general $|m|\le l$.
Because of this change, in the sentence just below
(14.30.2), “*tesseral* for $$ and
*sectorial* for $m=l$” has been replaced with “*tesseral* for
$$ and *sectorial* for $|m|=l$”. Furthermore, in
(14.30.4), $m$ has been replaced with $|m|$.

*Reported by Ching-Li Chai on 2019-10-05*

The range of $x$ was extended to include $1$. Previously this equation appeared without the order estimate as ${I}_{x}(a,b)\sim \frac{\mathrm{\Gamma}\left(a+b\right)}{\mathrm{\Gamma}\left(a\right)}{\sum}_{k=0}^{\mathrm{\infty}}{d}_{k}{F}_{k}$.

*Reported 2016-08-30 by Xinrong Ma.*

Two corrections have been made in this paragraph. First, the correct range of the initial displacement $a$ is $$. Previously it was $\sqrt{1/\beta}\le |a|\le \sqrt{2/\beta}$. Second, the correct period of the oscillations is $2K\left(k\right)/\sqrt{\eta}$. Previously it was given incorrectly as $4K\left(k\right)/\sqrt{\eta}$.

*Reported 2014-05-02 by Svante Janson.*