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BEGIN:VEVENT
UID:ea78703eb9919c80219000610c318352
CATEGORIES:Experimental Mathematics Seminar
CREATED:20211007T113747
SUMMARY:Accelerating hypergeometric indefinite summation
LOCATION:Zoom 
DESCRIPTION:<p><em style="color: #000000; font-family: 'Times New Roman'; font-size: me
 dium; background-color: inherit;">Abstract</em>: One well-known longstandin
 g problem with Gosper’s algorithm is that its running time depends at lea
 st linearly on the dispersion of the rational certificate of the summand, a
 nd this last can be exponentially large in the bit size of the summand. Thi
 s makes summation problems for hypergeometric terms with large dispersion v
 alues effectively intractable. We show that for summable terms this depende
 ncy is not essential (can be removed). The structure of polynomial solution
 s to the Gospe key equation is analyzed. A method for rapid extractionsof s
 imple high-degree factors of the solution is given. Resulting modified Gosp
 er's algorithm is presented. This result is based on very simple and well-k
 nown facts, properties, and lazy evaluation rules of factorial polynomials.
  Experimental Maple implementation confirms practical acceleration in compu
 ting of indefinite sums and rational normal forms of hypergeometric terms.<
 /p>
CONTACT:Eugene Zima, Wilfrid Laurier University
X-EXTRAINFO: Zoom Link https://rutgers.zoom.us/j/94346444480 [password: The 20th Catala
 n number, alias (40)!/(20!*21!), alias 6564120420 ]
DTSTAMP:20260827T105516
DTSTART;TZID=America/New_York:20211028T170000
DTEND;TZID=America/New_York:20211028T180000
SEQUENCE:0
TRANSP:OPAQUE
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