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Invited Speaker Frank Garvan Professor University of Florida Gainesville, FL |
Email: |
frank@math.ufl.edu |
Homepage: |
http://www.math.ufl.edu/~frank/ |
Paper: |
Approximations to Pi via the Dedekind Eta function |
Talk: |
Approximations to Pi via the Dedekind Eta function
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Abstract: |
Arguably the most efficient algorithm currently known for the
extended precision calculation of Pi is a quartic iteration due
to J.M. and P.B. Borwein. In their paper, the Borweins show
how this iteration and others are intimately connected to the
work of Ramanujan. This connection is shown utilizing their
alpha-function which is defined in terms of theta-functions.
They are able to find the p-th order iterations based on this
function using modular equations for the theta-functions. In
this paper we construct an infinite family of alpha functions.
Each one gives rise to a p-th order iteration. For p=4 we obtain an
iteration related to the Borwein quartic iteration. For p=3
we obtain a cubic iteration due to the Borweins but does not
come from the alpha-function. For p=7 we find a septic iteration
that is analogous to the cubic iteration. Our method depends
on using the computer and a symbolic algebra package to find
and solve certain modular equations.
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Born: |
Australia |
Education: |
1973-1976: Undergraduate study in Pure Mathematics,
at the University of New South Wales, Kensington,
Australia.
1977: Dip. Ed.
1981-1982: Masters degree in Mathematics at the University
of New South Wales under the supervision of Mike
Hirschhorn.
1983-1986: PhD in Mathematics at the Pennsylvania State
University under the supervision of George Andrews.
1987: Postdoc at University of Wisconsin, under the supervision
of Richard Askey.1988: Postdoc at the IMA, University of Minnesota.1988-1989: Postdoc at Macquarie University, North Ryde,
Australia under supervision of John Loxton.
1990: Postdoc at Dalhousie University, Halifax, Nova Scotia
under the supervision of Jon and Peter Borwein.
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Family: |
Frank. Cyndi - charming roomate.
Jeffrey - likes to play all electric appliances very loudly.
Gerard - likes to weave home-made hammocks in the backyard.
Maggie - keeps everyone in line.
Morton, Zac and Summer - our corgies.
Simba - our cat that thinks she's a dog.
Fluffster - deceased (pet rabbit).
Ziggy - deceased (pet hamster).
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Interests: |
Frank's hobbies include banging his eighty-eights, backyard
pit digging and tunnel construction. Also, he does a little
story-telling on the side:
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Comments: |
A sucessful day: (1) Getting home safely,
(2) Eating a good meal,
(3) Watching "Dumb and Dumber",
(4) Taking the dogs for a walk
and not getting yelled at by the
neighbors,
(5) Finding that 2x4 to lock the
bedroom door.
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