- #1
alphy
- 1,403
- 1
Hi,
When I was younger, a teacher of mine gave me
this problem for training:
http://perso.wanadoo.fr/eric.chopin/pbX_en.htm
This was a test for the admission to a well known
french Engineering School. What was interesting was that
the test contains a question that was unsolved at the
time this examination was given. If someone has the solution,
I'm very interested to know it.
Summary: the goal is to find a solution of
xy''+2y' +x/y=0 defined on [0,1] such that y(1)=e where e is a
given real number. For that purpose one sets g_0=e and
g_{n+1} = e+T(1/g_n) where
T(f)(x) = (1/x-1)\int_0^x t^2f(t)dt + \int_x^1 (t-t^2)f(t)dt
g_{2p} converges to g and g_{2p+1} converges to G. The open
question is to show that g=G ...
Any idea is welcome
When I was younger, a teacher of mine gave me
this problem for training:
http://perso.wanadoo.fr/eric.chopin/pbX_en.htm
This was a test for the admission to a well known
french Engineering School. What was interesting was that
the test contains a question that was unsolved at the
time this examination was given. If someone has the solution,
I'm very interested to know it.
Summary: the goal is to find a solution of
xy''+2y' +x/y=0 defined on [0,1] such that y(1)=e where e is a
given real number. For that purpose one sets g_0=e and
g_{n+1} = e+T(1/g_n) where
T(f)(x) = (1/x-1)\int_0^x t^2f(t)dt + \int_x^1 (t-t^2)f(t)dt
g_{2p} converges to g and g_{2p+1} converges to G. The open
question is to show that g=G ...
Any idea is welcome