**T. K. Pogány **

## Local Growth of
Weierstrass s-Function and Whittaker-Type Derivative
Sampling

**abstract:**

Two explicit guard functions $K_j = K_j(\delta_z)$, $j=1,2$, are obtained, which
depend on the distance $\delta_z$ between $z$ and the nearest point of the
integer lattice in the complex plane, such that $\delta_z K_1(\delta_z) \leq |\sigma(z)|e^{-\pi
|z|^2/2} \leq \delta_z K_2(\delta_z),\; z\in {\mathbb C}$, where $\sigma(z)$
stands for the Weierstraß $\sigma$-function.
This result is used to improve the circular truncation error upper bound in the
$q$-th order Whittaker-type derivative sampling for the Leont'ev functions space
$[2, \frac{\pi q}{2})$, $q\geq 1$.