based on Sinc functions

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1: 3.3 Interpolation
For interpolation of a bounded function $f$ on $\mathbb{R}$ the cardinal function of $f$ is defined by …
2: Bibliography S
• F. Stenger (1993) Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.
4: 3.4 Differentiation
For formulas for derivatives with equally-spaced real nodes and based on Sinc approximations (§3.3(vi)), see Stenger (1993, §3.5). …
§3.4(ii) Analytic Functions
3.4.18 $\frac{1}{k!}\,f^{(k)}(x_{0})=\frac{1}{2\pi r^{k}}\int_{0}^{2\pi}f(x_{0}+re^{i% \theta})e^{-ik\theta}\,\mathrm{d}\theta.$
3.4.19 $\frac{1}{k!}=\frac{1}{2\pi r^{k}}\int_{0}^{2\pi}e^{r\cos\theta}\cos\left(r\sin% \theta-k\theta\right)\,\mathrm{d}\theta.$
5: 33.11 Asymptotic Expansions for Large $\rho$
33.11.1 ${H^{\pm}_{\ell}}\left(\eta,\rho\right)\sim e^{\pm\mathrm{i}{\theta_{\ell}}% \left(\eta,\rho\right)}\sum_{k=0}^{\infty}\frac{{\left(a\right)_{k}}{\left(b% \right)_{k}}}{k!(\pm 2\mathrm{i}\rho)^{k}},$
6: 25.11 Hurwitz Zeta Function
25.11.30 $\zeta\left(s,a\right)=\frac{\Gamma\left(1-s\right)}{2\pi i}\int_{-\infty}^{(0+% )}\frac{e^{az}z^{s-1}}{1-e^{z}}\,\mathrm{d}z,$ $s\neq 1$, $\Re a>0$,
25.11.37 $\sum_{k=1}^{\infty}\frac{(-1)^{k}}{k}\zeta\left(nk,a\right)=-n\ln\Gamma\left(a% \right)+\ln\left(\prod_{j=0}^{n-1}\Gamma\left(a-e^{(2j+1)\pi i/n}\right)\right),$ $n=2,3,4,\dots$, $\Re a\geq 1$.
7: 4.45 Methods of Computation
Logarithms
and since $|y|\leq\frac{1}{2}\ln 10=1.15\dots$, $e^{y}$ can be computed straightforwardly from (4.2.19).
Trigonometric Functions
and since $|\theta|\leq\frac{1}{2}\pi=1.57\dots$, $\sin\theta$ and $\cos\theta$ can be computed straightforwardly from (4.19.1) and (4.19.2). …
8: 25.15 Dirichlet $L$-functions
§25.15 Dirichlet $L$-functions
When $\chi$ is a primitive character (mod $k$) the $L$-functions satisfy the functional equation: …
§25.15(ii) Zeros
Since $L\left(s,\chi\right)\neq 0$ if $\Re s>1$, (25.15.5) shows that for a primitive character $\chi$ the only zeros of $L\left(s,\chi\right)$ for $\Re s<0$ (the so-called trivial zeros) are as follows: …
9: 1.16 Distributions
$\Lambda:\mathcal{D}(I)\rightarrow\mathbb{C}$ is called a distribution, or generalized function, if it is a continuous linear functional on $\mathcal{D}(I)$, that is, it is a linear functional and for every $\phi_{n}\to\phi$ in $\mathcal{D}(I)$, … Since $\delta_{x_{0}}$ is the Lebesgue–Stieltjes measure $\mu_{\alpha}$ corresponding to $\alpha(x)=H\left(x-x_{0}\right)$ (see §1.4(v)), formula (1.16.16) is a special case of (1.16.3_5), (1.16.9_5) for that choice of $\alpha$. … Since $\sqrt{2\pi}\mathscr{F}\left(\delta\right)=1$, we have …Since the quantity on the extreme right of (1.16.41) is equal to $\sqrt{2\pi}\left\langle\delta,\phi\right\rangle$, as distributions, the result in this equation can be stated as …
10: 2.3 Integrals of a Real Variable
For the function $\Gamma$ see §5.2(i). This result is probably the most frequently used method for deriving asymptotic expansions of special functions. Since $q(t)$ need not be continuous (as long as the integral converges), the case of a finite integration range is included. … Another extension is to more general factors than the exponential function. …
• (d)

If $p(b)=\infty$, then $P_{0}(b)=0$ and each of the integrals

2.3.22 $\int e^{ixp(t)}P_{s}(t)p^{\prime}(t)\,\mathrm{d}t,$ $s=0,1,2,\dots$,

converges at $t=b$ uniformly for all sufficiently large $x$.