example sum

Available Software:

  • Sigma, a Mathematica package for discovering and proving multi-sum identities based on difference fields (by C. Schneider)

  • HarmonicSums, a Mathematica package for allows to deal with nested sums such as harmonic sums, S-sums, cyclotomic sums and cyclotmic S-sums as well as iterated integrals such as harmonic polylogarithms, multiple polylogarithms and cyclotomic polylogarithms in an algorithmic fashion (by J. Ablinger).

  • EvaluateMultiSums, a Mathematica package for the simplification of definite multi-sums in terms of indefinite nested sums and products (by C. Schneider).

    SumProduction, a Mathematica package for handling large scale problems in terms of multi-sums. This package requires EvaluateMultiSums and Sigma (by C. Schneider; in preparation).

  • MultiIntegrate, a Mathematica package for computing multiple integrals (by J. Ablinger).

  • PLDESolver, a Mathematica package for solving non-degenerated parameterized linear difference equations in difference rings with zero-divisors (by J. Ablinger and C. Schneider).
  • RhoSum, experimental code of a Mathematica package for a Refined HOlonomic SUmmation based on difference field theory (by M. Round; in preparation).

  • SolveCoupledSystem, a Mathematica package for solving coupled systems of differential and difference equations in terms of nested sums and products (by C. Schneider, in preparation).
  • FSums, a Mathematica package for evaluting multi-sums (by F. Stan, in preparation).