BBP formulae and expansion
Note : Gery Huvent
just started his own personal website which I invite you to discover (Though its
in French). You can contact him at this adresse.
A Mountain of Formulae !
I cna't put them all
up, there's too many of them! You will discover them throughtout
reading the exploration of hypergeometric and
harmonic series around Pi which they come from. But, by noting the sum , for , let's write down among others :
Gery Huvent, passionated
Gery Huvent completly
deserve this page since his contribution to the understanding of BBP
series is important. To make you feel for his life, (and for once we
can show a mathematician in his stong years!) here are a few elements
of his biography.
For the moment, Gery Huvent is part of the mathematics department of
the University of Lille, where he teach "prepa" students (this is
roughly the French equivalent of first year at university, although its
a year to get them ready for uni). But before he got there....
Gery Huvent was born in (obviously) tormented times on may the 8th
1968, day that allows him to still celebrate peacefully his birthday!
Born of chemist parents into a big family (4 siblings!), Gery let his
scholl days flow by, mellow without being brilliant, until "la seconde"
(Year 11). Then discovering the forgoten wonders of microcomputing
(TO7, Amstrad !!), he show a real interest for programming and physics.
Maths were still far away!
And yet, as he told us himself "I had hopes to win the Loto then. To
calculate my chances, I (re)discovered Pascal's triangle. Of course I
only realised later on...." Don't we all wish we were at that stage! :-)
to maths, while very discrete, happened in "terminal" (Year 13), often
the time where most mathematician start to work.... And since we all
end up, one day or the other, taken by the magic of Pi, Gery then
discover the spigot algorithm whle programing for its decimals!
According to legends when he frown, a Pi appear on his forhead, like Malraux. Pi strikes again! There some
things that deeply established....
Completing his definite conversion to math in "prepa", he goes to
SupAero after a few health problem that stop him from taking an (maybe)
even more prestigious exam!
Luckly, talent is never forgotten.... fighting a bit during those years
(although mpstly having no problem!), he then go to Lille, gets married
to an old school friend, and takes a maths DEA which is not great from
a opportunity point of view even with his good results. This is when he
pass the agreg and gets a brilliant 35th!
After a transitional
year in Bourges, he is now definitly in Lille. Three children later, he
is the father of a happy family that is fascinated by maths which
honors his ideas and his enthusiam for our favourite little constant!
Forever absent minded, clumsy and guillible as he like to say it, Gery
Huvent represent all the sincerity and the natural we can hope from an
very engaging man. Rare are those that are interested in others and
conscious of there place, whether in society or more generally in
nature. Gery is one of those, even if is friendship is hard to gain! Misanthropic and
humanist at the same time, as he defines himself, the society of men
never really satisfied him. Constantly tangled up in impossible mess
with all his electonical or mechanical intrument that comes near him
and just break down, never give him you video player if you don't want
him to turn it into a coffee machine!
Lover of black and weird humor, british humor, his favourite literature
is a clever mix of wonders, demons and melancholy (Dorian Gray, Alice
in wonderland, Demons and wonders of Lovecraft, or Beauty and Sadness
by Kawabata) but also maths by Knuth.
And never ask him for the time, he doesn't have a watch !
A little story to finish off, in his absent minded days, that Gery tell
"During a medical visit before an exam for Polytechnique. I arrive
thinking of other things (Maths), I take the file and fill it. I go and
see the doctor and he then tell me:
- You are very absent minded
I reply that no, not that much.
He then ask me
- You name, is really Name, and your surname is Surname?"
Around , the BBP formulae, binomials, harmonic...
The work by Gery
Huvant is varied (geometry, analysis) but we are mainly going to
concentrate here on the marvelous help he did on the BBP series,
binomial and harmonic. We can find his contribution in the exploration
of hypergeometric and harmonic series, which
he wrote nearly half of it directly. Those formulae, which sometime
seems not to be a completly controled territory by our favourites
mathematicians, in spite of their apparent simplicity, drags us to far
away lands, populated by BBP formulae, by
polylogarithmes, by polygamma, by binomial
series, harmonic series, all representation of a
type of hard to get integral: .
All the proves of the
above formulae are accesible in the pages of this site!
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