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Une formule de quadrature pour les fonctions entières de type exponentiel. (A quadrature formula for entire functions of exponential type). (French) Zbl 0589.30024
If $$0<\sigma <\infty$$ and f is an entire function of exponential type$$<2\sigma$$, or of type $$2\sigma$$ and $$f(x)=O(\exp (| x|^{- \delta}))$$, $$\delta >1$$, then $\int^{\infty}_{-\infty}f(x)dx=\pi \sigma^{-1}\sum^{\infty}_{-\infty}f(n\pi /\sigma).$ These results could be deduced from the Poisson summation formula, but the authors’ proof is based on L. Hörmander’s approximation method [Math. Scand. 3, 21-27 (1955; Zbl 0065.303)].
Reviewer: R.P.Boas

##### MSC:
 30D20 Entire functions of one complex variable, general theory 65D30 Numerical integration 65B15 Euler-Maclaurin formula in numerical analysis