Built on

J. Symbolic Comput
Original
D. Zeilberger · 1991
Earlier work this paper cites.
In J. von zur Gathen, editor, Proc. ISSAC’94
S.A. Abramov and M. Petkovšek · 1994
Earlier work this paper cites.
Master’s thesis, RISC, J. Kepler University, Linz, 1996
C. Mallinger · 1996
Earlier work this paper cites.
A = B A=B
M. Petkovšek, H. S. Wilf, and D. Zeilberger · 1996
Earlier work this paper cites.
J. Blümlein and S. Kurth, Phys. Rev
1999
Earlier work this paper cites.
S. Moch, P. Uwer and S. Weinzierl, J. Math. Phys
2002
Earlier work this paper cites.
J. Differ. Equations Appl
C. Schneider · 2005
Earlier work this paper cites.
Ann. Comb
C. Schneider · 2005
Earlier work this paper cites.
J. Blümlein, A. De Freitas, W. L. van Neerven and S. Klein, Nucl. Phys
2006
Earlier work this paper cites.
I. Bierenbaum, J. Blümlein and S. Klein, Nucl. Phys
2007
Earlier work this paper cites.

Similar

I. Bierenbaum, J. Blümlein and S. Klein, PoS ACAT
2007
Cited alongside, same era.
Sem. Lothar. Combin
C. Schneider · 2007
Cited alongside, same era.
I. Bierenbaum, J. Blümlein, S. Klein and C. Schneider, Nucl. Phys
Original
2008
Cited alongside, same era.
J. Symbolic Comput
Original
C. Schneider · 2008
Cited alongside, same era.
I. Bierenbaum, J. Blümlein and S. Klein, Nucl. Phys
Original
2009
Cited alongside, same era.
I. Bierenbaum, J. Blümlein and S. Klein, Phys. Lett
Original

Then

In: Motives, quantum field theory, and pseudodifferential operators
Original
J. Blümlein, Comput. Phys. Commun · 2010
Later among the works it cites.
J. Blümlein, D. J. Broadhurst and J. A. M. Vermaseren, Comput. Phys. Commun
Original
2010
Later among the works it cites.
In Motives, quantum field theory, and pseudodifferential operators
Original
C. Schneider · 2010
Later among the works it cites.
Ann. Comb
Original
C. Schneider · 2010
Later among the works it cites.
J. Ablinger, J. Blümlein and C. Schneider, J. Math. Phys
Original
2011

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Reading the bibliography…

2012

Evaluation of Multi-Sums for Large Scale Problems

Blümlein, J., Hasselhuhn, A., Schneider, C.

Understand

A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums.

In this article, we present a general summation method based on difference fields that simplifies these multi--sums by transforming them from inside to outside to representations in terms of indefinite nested sums and products.
In particular, we present techniques that assist in the task to simplify huge expressions of such multi-sums in a completely automatic fashion.
The ideas are illustrated on new calculations coming from 3-loop topologies of gluonic massive operator matrix elements containing two fermion lines, which contribute to the transition matrix elements in the variable flavor scheme.

Built on

J. Symbolic Comput
Original
D. Zeilberger · 1991
Earlier work this paper cites.
In J. von zur Gathen, editor, Proc. ISSAC’94
S.A. Abramov and M. Petkovšek · 1994
Earlier work this paper cites.
Master’s thesis, RISC, J. Kepler University, Linz, 1996
C. Mallinger · 1996
Earlier work this paper cites.
A = B A=B
M. Petkovšek, H. S. Wilf, and D. Zeilberger · 1996
Earlier work this paper cites.
J. Blümlein and S. Kurth, Phys. Rev
1999
Earlier work this paper cites.
S. Moch, P. Uwer and S. Weinzierl, J. Math. Phys
2002
Earlier work this paper cites.
J. Differ. Equations Appl
C. Schneider · 2005
Earlier work this paper cites.
Ann. Comb
C. Schneider · 2005
Earlier work this paper cites.
J. Blümlein, A. De Freitas, W. L. van Neerven and S. Klein, Nucl. Phys
2006
Earlier work this paper cites.
I. Bierenbaum, J. Blümlein and S. Klein, Nucl. Phys
2007
Earlier work this paper cites.