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UID:f927bef400938a0761668b099b3b7fee
CATEGORIES:Experimental Mathematics Seminar
CREATED:20230118T091116
SUMMARY:Gosper's algorithm and Bell numbers
LOCATION:Zoom
DESCRIPTION:Abstract: Computers are now very good at evaluating finite sums in closed f
 orm. They can do them almost instantly and can often prove that a sum canno
 t be evaluated in closed form, like the partial sums of k!. Just like in ca
 lculus, we can fix summands that don't yield closed forms by multiplying th
 em by a suitable "summation factor." I will show that this idea, applied to
  sums of falling factorials, produces sequences of polynomials closely rela
 ted to the Bell numbers.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="color: #000000; font-family: 'Times New Roman'; font-size: medium
 ; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; 
 text-indent: 0px; text-transform: none; white-space: normal; widows: 2; wor
 d-spacing: 0px;"><em>Abstract</em>: Computers are now very good at evaluati
 ng finite sums in closed form. They can do them almost instantly and can of
 ten prove that a sum cannot be evaluated in closed form, like the partial s
 ums of k!. Just like in calculus, we can fix summands that don't yield clos
 ed forms by multiplying them by a suitable "summation factor." I will show 
 that this idea, applied to sums of falling factorials, produces sequences o
 f polynomials closely related to the Bell numbers.</p>
CONTACT:Robert Dougherty-Bliss, Rutgers University
X-EXTRAINFO:Zoom Link: https://rutgers.zoom.us/j/94346444480\npassword: The 20th Catala
 n number, alias (40)!/(20!*21!), alias 6564120420 ]
DTSTAMP:20260826T212755
DTSTART;TZID=America/New_York:20230216T170000
DTEND;TZID=America/New_York:20230216T180000
SEQUENCE:0
TRANSP:OPAQUE
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