All formulas
Num. approx.
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Delirium !

Boris Gourévitch
The world of Pi - V2.57
modif. 13/04/2013

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BBP formulae and expansion
G. Huvent

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 BBPk  (a,b,P (y))  the sum  sum o o  1 ( sum b -2  a    )
  i=0 ai   l=0 (bi+l+l1)k+1- , for P (y) = a0 + a1y +...+ ab-2yb-2  , let's write down among others :

Gery Huvent, passionated by maths

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! :-)
metamorphosis 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 us:
"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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