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SUMMARY:Divergent series: from Thomas Bayes’s bewilderment to today’s 
 resurgence via the rainbow - Michael Berry (Bristol)
DTSTART:20141119T141500Z
DTEND:20141119T151500Z
UID:TALK54642@talks.cam.ac.uk
CONTACT:Mahdi Godazgar
DESCRIPTION:Following the discovery by Bayes in 1747 that Stirling’s ser
 ies for the factorial is\ndivergent\, the study of asymptotic series has t
 oday reached the stage of enabling\nsummation of the divergent tails of ma
 ny series with an accuracy far beyond that of\nthe smallest term. Several 
 of these advances sprang from developments of Airy’s\ntheory of waves ne
 ar optical caustics such as the rainbow. Key understandings by\nEuler\, St
 okes\, Dingle and Écalle unify the different series corresponding to diff
 erent\nparameter domains\, culminating in the concept of resurgence: quant
 ifying the way in\nwhich the low orders of such series reappear in the hig
 h orders.
LOCATION:MR2\, Centre for Mathematical Sciences
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