A Symbolic Summation Approach to Find Optimal Nested Sum Representations

N.E. Nörlund, Differenzenrechnung , Springer, Berlin, 1924

1924

Earlier work this paper cites.

R.W. Gosper, Decision procedures for indefinite hypergeometric summation , Proc. Nat. Acad. Sci. U.S.A. 75

1978

Earlier work this paper cites.

M. Karr, Summation in finite terms , J. ACM 28

1981

Earlier work this paper cites.

B. Buchberger and R. Loos, Algebraic Simplification , Computer Algebra - Symbolic and Algebraic Computation (B. Buchberger, G. E. Collins, and R. Loos, eds.), Springer, Vienna - New York, 1982, pp. 11–43

1982

Earlier work this paper cites.

by same author, Theory of summation in finite terms , J. Symbolic Comput. 1

1985

Earlier work this paper cites.

D. Zeilberger, The method of creative telescoping , J. Symbolic Comput. 11

1991

Earlier work this paper cites.

S.A. Abramov and M. Petkovšek, D’Alembertian solutions of linear differential and difference equations , Proc. ISSAC’94 (J. von zur Gathen, ed.), ACM Press, 1994, pp. 169–174

1994

Earlier work this paper cites.

M. Petkovšek, H. S. Wilf, and D. Zeilberger, a = b a=b , A. K. Peters, Wellesley, MA, 1996

1996

Earlier work this paper cites.

I. Nemes and P. Paule, A canonical form guide to symbolic summation , Advances in the Design of Symbolic Computation Systems (A. Miola and M. Temperini, eds.), Texts Monogr. Symbol. Comput., Springer, Wien-New York, 1997, pp. 84–110

1997

Earlier work this paper cites.

P. Paule and A. Riese, A Mathematica q-analogue of Zeilberger’s algorithm based on an algebraically motivated aproach to q q -hypergeometric telescoping , Special Functions, q-Series and Related Topics (M. Ismail and M. Rahman, eds.), vol. 14, Fields Institute Toronto, AMS, 1997, pp. 179–210

1997

Earlier work this paper cites.

J. Blümlein and S. Kurth, Harmonic sums and Mellin transforms up to two-loop order , Phys. Rev. D60

1999

Earlier work this paper cites.

A. Bauer and M. Petkovšek, Multibasic and mixed hypergeometric Gosper-type algorithms , J. Symbolic Comput. 28

1999

Cited alongside, same era.

P.A. Hendriks and M.F. Singer, Solving difference equations in finite terms , J. Symbolic Comput. 27

1999

Cited alongside, same era.

C. Schneider, Symbolic summation in difference fields , Ph.D. thesis, RISC-Linz, J. Kepler University, Linz, May 2001

2001

Cited alongside, same era.

S. Moch, P. Uwer, and S. Weinzierl, Nested sums, expansion of transcendental functions, and multiscale multiloop integrals , J. Math. Phys. 6

2002

Cited alongside, same era.

by same author, Gosper’s algorithm, accurate summation and the discrete Newton–Leibniz formula , Proc. ISSAC’05 (M. Kauers, ed.), ACM, 2005, pp. 5–12 (english)

2005

Cited alongside, same era.

S. Moch and C. Schneider, Feynman integrals and difference equations , Proc. ACAT 2007, vol. PoS(ACAT)083, 2007, [arXiv:hep-ph/0709.1769]

2007

Later among the works it cites.

by same author, Symbolic summation assists combinatorics , Sém. Lothar. Combin. 56

2007

Later among the works it cites.

I. Bierenbaum, J. Blümlein, S. Klein, and C. Schneider, Two–loop massive operator matrix elements for unpolarized heavy flavor production to o ⁡ ( e ​ p ​ s ​ i ​ l ​ o ​ n ) o(epsilon) , Nucl.Phys. B 803

2008

Later among the works it cites.

by same author, A refined difference field theory for symbolic summation , J. Symbolic Comput. 43

Original

2008

Later among the works it cites.

J. Blümlein, M. Kauers, S. Klein, and C. Schneider, Determining the closed forms of the O ⁡ ( a s 3 ) O(a_{s}^{3}) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra , Tech. Report DESY 09-002, SFB/CPP-09-22, Deutsches Elektronen Syncrothron, Zeuthen, 2009, [arXiv:hep-ph/0902.4091]