Evaluation of the fourier transform of e(-ux2) for imaginary U
Abstract
It is shown that the Fourier integral of the function exp(-ux(2)) exists not only for u satisfying Re u gt 0 but also for u that satisfies Re u >= 0. The proof is given by evaluating this integral for imaginary u.
Keywords:
Fourier transform / Cauchy's residue theorem / Fresnel's integrals / wave function behind a grating / interference of matter wavesSource:
Journal of Russian Laser Research, 2006, 27, 3, 220-224Publisher:
- Springer Science and Business Media Deutschland GmbH
Funding / projects:
- Govorna komunikacija čovek-mašina (RS-11001)
DOI: 10.1007/s10946-006-0010-3
ISSN: 1071-2836