# Symbolic Summation II, Summer 2008

## Description

In this lecture we focus on two main problems.
I. We present algorithms that represent indefinite nested sums and products in an optimal way in difference fields.

In order to accomplish this task, we refine M. Karr's difference field theory of PiSigma-fields.

II. Given such sum-product expressions in the difference field setting, we shall present algorithms that
enable to

- simplify nested sums (indefinite summation)
- compute recurrences (Zeilberger's creative telescoping)
- solve recurrences (with sum extensions).

All three components combined deliver strong tools in order to compute closed forms of summation problems.
We will illustrate this algorithmic machinery with typical examples, e.g., from combinatorics and particle physics.

**Place:** Seminarraum Schloss Hagenberg

05.03. |
** 16:15-17:45 ** |

12.03. |
** No lecture ** |

02.04. |
** 14:00 - 15:30 ** |

09.04. |
** No lecture ** |

16.04. |
** Blocked lecture (14:00 - 18:00) ** |

23.04 |
** No lecture ** |

30.04. |
** No lecture ** |

07.05. |
** No lecture ** |

14.05. |
** 16:15 - 17:45** |

21.05. |
** 16:15-17:45 ** |

28.05. |
** 16:15-17:45 ** |

04.06. |
** Blocked lecture (14:00 - 18:00) ** |

11.06. |
** No lecture** |

18.06. |
** 16:15 - 17:45 ** |

25.06. |
** No lecture ** |

In July we will have an extra meeting with a blocked lecture (~6 hours).