
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

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
alphafunction which is defined in terms of thetafunctions.
They are able to find the pth order iterations based on this
function using modular equations for the thetafunctions. In
this paper we construct an infinite family of alpha functions.
Each one gives rise to a pth 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 alphafunction. 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.

Born: 
Australia 
Education: 
19731976: Undergraduate study in Pure Mathematics,
at the University of New South Wales, Kensington,
Australia.
1977: Dip. Ed.
19811982: Masters degree in Mathematics at the University
of New South Wales under the supervision of Mike
Hirschhorn.
19831986: 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.19881989: 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.

Family: 
Frank. Cyndi  charming roomate.
Jeffrey  likes to play all electric appliances very loudly.
Gerard  likes to weave homemade 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).

Interests: 
Frank's hobbies include banging his eightyeights, backyard
pit digging and tunnel construction. Also, he does a little
storytelling on the side:

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.
