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A multidimensional Jordan residue lemma with an application to Mellin-Barnes integrals

  • Mikael Passare
  • August Tsikh
  • Oleg Zhdanov
Chapter
Part of the Aspects of Mathematics book series (ASMA, volume E 26)

Abstract

The classical Jordan lemma states that if a function ψ is continuous on the real axis with a holomorphic continuation to the upper half plane Π+ = { z = x + iy;y > 0} except for a finite number of points {a} ⊂ Π+, and if ψ(z) tends to zero as |z| → ∞ in the closed half plane Π+, then
$$ \int_{ - \infty }^\infty {\psi (x){e^{iax}}dx = 2\pi i\sum\limits_{\left\{ a \right\}} {re{s_a}\;\omega ,} } $$
(0.1)
where α is an arbitrary positive number and ω denotes the differential form ψ(z)e iaz dz.

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Bibliography

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Copyright information

© Springer Fachmedien Wiesbaden 1994

Authors and Affiliations

  • Mikael Passare
  • August Tsikh
  • Oleg Zhdanov

There are no affiliations available

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