By Tracy Kompelien
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Title: 2-D Shapes Are in the back of the Drapes!
Author: Kompelien, Tracy
Publisher: Abdo Group
Publication Date: 2006/09/01
Number of Pages: 24
Binding sort: LIBRARY
Library of Congress: 2006012570
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Extra resources for 2-D Shapes Are Behind the Drapes!
1313.  F. B ROWN, Commun. Math. Phys. 1660.  F. 0114.  F. B ROWN and K. 5429.  O. 2856.  O. 0905.  P. A LUFFI and M. M ARCOLLI, Commun. Num. Theor. Phys. 1690.  P. A LUFFI and M. 2514. 24 Christian Bogner and Stefan Weinzierl  P. A LUFFI and M. 2107.  P. A LUFFI and M. 3225.  C. B ERGBAUER , R. B RUNETTI and D. 0633.  S. L APORTA, Phys. Lett. B549, 115 (2002), hep-ph/0210336.  S. L APORTA and E. R EMIDDI, Nucl. Phys. B704, 349 (2005), hepph/0406160.
To sum up all residues which lie inside the contour it is useful to know the residues of the Gamma function: (−1)n , n! (−1)n res ( (−σ + a), σ = a + n) = − . n! 5) In general there are multiple contour integrals, and as a consequence one obtains multiple sums. >i k >0 1 m1 ... 1 ik mk . >i k xkik x1i1 . . 8) k is called the depth of the Z -sum and w = m 1 + ... + m k is called the weight. , xk ). 9) For x1 = ... ,m k (n). 10) For n = ∞ and x1 = ... ,m k . 11) 22 Christian Bogner and Stefan Weinzierl The usefulness of the Z -sums lies in the fact, that they interpolate between multiple polylogarithms and Euler-Zagier sums.
13 Hence the question: how many irreducibles (let us call that number Dd,r ) must one pick in each cell of degree d and length r to get a complete and free system of irreducibles? The so-called BK-conjectures,14 which were formulated in 1996 (they applied to the genuine rather than formal multizetas, and resulted from purely numerical tests) suggest a startlingly complicated formula for Dd,r but no plausible rationale for its strange form. Soon after that, we published in  a convincing explanation for the formula, which however went largely unnoticed.