First Written: Dec. 8, 2004.

This version: Aug. 15, 2005.

This is a much improved, and much sharper redoing of multi-WZ theory! It is written in a very terse style, and some of the proofs are only sketched. It would be a very instructive excercise to fill-in the details.

• MultiZeilberger that computes recurrences and certificates for hypergeometric multiple sums.
• MultiZeilbergerDen that also computes recurrences and certificates for hypergeometric multiple sums, but the user has the freedom to assign denominators to the certificates, thereby having a chance to reduce the order of the recurrence.
• qMultiZeilberger that computes recurrences and certificates for q-hypergeometric multiple sums. It does what Axel Riese's Mathematica package does.
• MultiAlmkvistZeilberger that computes recurrences and certificates for hypergeometric (in fact hyper-exponential) multiple integrals.
• SMAZ that computes recurrences and certificates for hypergeometric (in fact hyper-exponential) multiple integrals that are SYMMETRIC in their variables.

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  SAMPLE Input and Output Files
  • For the Maple package MultiZeilberger
    • The input     yields the output.
    • The input     yields the output.
  • For the Maple package MultiZeilbergerDen
    • The input     yields the output    
  • For the Maple package qMultiZeilberger
    • The input     yields the output    
  • For the Maple package MultiAlmkvistZeilberger
    • The input     yields the output    
    • The input     yields the output    
    • The input ;  ;  yields the output    
    • The input     yields the output    
    • The input ;  ;  yields the output    
    • The input ;  ;  yields the output    
  • For the Maple package SMAZ
    • The input (for the diagonal coefficients of the rational function 1/(1-x-y-z+4xyz))     yields the output    
    • The input (for the 3D Mehta integral)     yields the output    

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