Abstract.
We obtain asymptotic expansions for the integral¶¶\( G_\nu(\omega,\lambda)=\omega\int_0^\infty \exp [i\omega t-\lambda (1-\cos t)- {1\over2}\nu t^2] dt, \)¶for large values of \(\omega\) and \(\lambda\) and \(\nu\rightarrow 0+\). For positive real parameters, the real part of the integral is associated with an exponentially small expansion in which the leading term involves a Jacobian theta function as an approximant. The asymptotic expansions are compared with numerically computed values of \(G_\nu(\omega,\lambda)\).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Author information
Authors and Affiliations
Additional information
Received: March 11, 1997
Rights and permissions
About this article
Cite this article
Paris, R. The asymptotic expansion of Gordeyev's integral. Z. angew. Math. Phys. 49, 322–338 (1998). https://doi.org/10.1007/PL00001486
Issue Date:
DOI: https://doi.org/10.1007/PL00001486