@article {Tuck2005,
 author="E.O. Tuck",
 title={Riemann--Siegel sums via stationary phase},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="2",
 pages="325--328",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="27th July, 2005",
 classmath="33E20, 41A60",
 publisher={AMPAI, Australian Mathematical Society},
 MRnumber="MR2183413",
 ZBLnumber="02246394",
 url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5212-Tuck/index.shtml",
 acknowledgement={I thank Jim Hill for discussions of this topic.},
 abstract={ A new representation is obtained for the Riemann $\xi $ function, in the form of a series of integrals, multiplied by an exponential factor capturing the correct decay rate for large imaginary argument. Each term in this series then has a simple stationary-phase asymptote, the total agreeing with the Riemann--Siegel sum. }
}