Dear Simon Plouffe

( and others )

I request investigating BBP - type formula's of the following type :

a = sum k = 0 .. oo [ ( b^k * p(k) * A(k) ) /q(k) ]

Where b is a gaussian rational ( Q(i) ) < 1.
p(k) and q(k) are polynomials with gaussian rational coefficients and A(k) is a vector of gaussian rationals.

The polynomials may or may not be factorable over the ring of gaussian rationals.

And it may or may not be a spigot algoritm.

Of course i am talking about non-trivial cases , where the real and imaginary parts cannot be easily rewritten as ordinary BBP-type formula's.

It would be nice to see such formula's for e.g.

zeta(3) + zeta(5) i

or

zeta(21)/zeta(7) where the imaginary part has vanished.
(assuming it can vanish in a non-trivial case )

I dont know if integer relation algoritms and its simple variants are sufficient to prove such identities.

I will leave choosing the name to Simon Plouffe himself.

Regards

Tommy1729

- Moving pairs

Given something like a checkers board, moving pairs would be checker
pieces
paired together and arranged on the board so they each checker piece
is said to be paired with another.

The pairs don't have to be next to eachother, they can arrange on the
board in any awy.

Any way arranged is fair for how this works, but it matters for how
they work.

There's no such thing as an empty space among pairs for how you
consider them together.

They are the idea of how they move, and the problem with finding how
to move them, and how they work being together.

- Moving a pair

Pick a pair to move.

Each of the pair is to move together at the same time.

A pair together can only move to another pair together.

In a recent thread Mike3 asked for a formula for the
coefficients of the powerseries for the U-tetration-
function. I looked again at this problem and made some
graphs, which are intended to give an impression about
some general characteristics of such powerseries.

You may look at

http://go.helms-net.de/math/tetdocs/CoefficientsUtFractionalHeight.htm

for some graphs and a short discussion.

(An older discussion of this, for the base t=exp(1), is here:
http://go.helms-net.de/math/tetdocs/CoefficientsForUTetration.htm )

Gottfried Helms

Hi, I am trying to deduce the general equation of the limacon (r=b+a
cos θ) from the geometry of rolling a circle around another circle of
equal radius, and watching how a 'generating point' moves that is
attached to the rolling circle.

I am getting stuck, and would be grateful for help with this!

Start with two circles of radius c, with diameters from (0,0) to (2c,
0) (fixed circle) and from (2c,0) to (4c,0) (moving circle). The
touching point is at (2c,0). The generating point starts at (3c+p,0),
i.e. a distance p to the right of the centre of the moving circle.

Now consider the position when the moving circle has rolled upwards so
that the line between the two circles' centres makes an angle t with
the polar axis. At this time, the generating point has polar
coordinates (r,θ).

I now need to eliminate t, to get an equation relating r to θ in terms
of c and p.

Any help would be appreciated!

Michael

Yesterday I had a discussion about the proof of the Banach-Steinhaus
Theorem (a.k.a. Uniform Boundedness Principle), which seems to me a typical
application of the Baire Category Theorem. I was told there does exist a
proof that does not use Baire, neither directly nor indirectly, but I have
been unable to find it. Does anyone happen to have a reference?

Best wishes,
Sebastiaan.

Dear NG,

I am just recently slowly trying to get myself involved in algebraic
topology and geometry dealing with polytopes.
Unfortunately I am in a situation where I do not have the luxury of
visiting a library until maybe after a few months when I am more
accustomed with the new city and new job I am in. So I will try to
rely a bit on this newsgroup :)

I know from my limited amount of books (I use the German book of
Forster, Analysis III) of what a generalized triangle is. A n-simplex
defined as linear combination of fixed n+1 point of R^n (with the
coefficients in R of this linear combinations must always be >= 0 and
must sum up to 1) .. in other words the convex hull of n+1 points in
R^n are simplexes.. I guess Im pretty ok with simplexes...

On Jul 11, 3:49 pm, rst0wxyz yahoo.com> wrote:

Consider the following equiation under the given conditions.

x^k + y^k = Ek^R (1)

Conditions: x, y, k, E, R are all integers each > 0
x, y are odd, k is a prime > 5, E is even.

Assertion: (1) cannot be satisfied under the given conditions.

If the assertion is correct I would appreciate some relevant
reference.

Highlighted text from the list
How to Become a Pure Mathematician (or Statistician):
a List of Undergraduate and Basic Graduate Textbooks and Lecture
Notes

Stage 1

Halmos P.R. Naive Set Theory
Graham R.L., Knuth D.E. and Patashnik O. Concrete Mathematics: A
Foundation for Computer Science
Hardy G.H. A Course of Pure Mathematics
Spivak M. Calculus

Stage 2

Shilov G.E. Linear Algebra
Courant R. and John F. Introduction to Calculus and Analysis II/1, II/
2
Brown J.W. and Churchill R.V. Complex Variables and Applications
Simmons G.F. and Krantz S.G. Differential Equations: Theory,
Technique, and Practice

Stage 3

The best way to evaluate the indefinite integral
∫ (3x^2 + 1)(5x^3 + 5x −12)^5 dx is
a. By expanding and applying the power rule
b. By substitution 5x3 + 5x − 12 = u
c. By substitution 3x 2 + 1 = u
I need little more explanation