An Integral Representation for the Polylogarithm Function and some Special Values

Integral representation of some functions related to the Gamma function

We prove that the functions Φ(x) = [Γ(x + 1)]1/x(1 + 1/x)x/x and log Φ(x) are Stieltjes transforms. 2000 Mathematics Subject Classification: primary 33B15; secondary 26A48

Some Special Values of Cosine

Multiple polylogarithm values at roots of unity

For any positive integer N let μN be the group of the N th roots of unity. In this note we shall study the Q-linear relations among the values of multiple polylogarithms evaluated at μN . We show that the standard relations considered by Racinet do not provide all the possible relations in the following cases: (i) level N = 4, weight w = 3 or 4, and (ii) w = 2, 7 <N < 50, and N is a power of 2 ...

Some Unusual Identities for Special Values of the Riemann Zeta Function ∗

In this paper, we use elementary methods to derive some new identities for special values of the Riemann zeta function.

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...