Examples Of The Markov-WZ Method

Examples Of The Markov-WZ Method
This page of examples accompanies the article The Markov-WZ Method By Mohamud Mohammed and Doron Zeilberger
Examples prepared: Aug. 3 , 2004.
All the examples here were generated by using procedures MarkovPaper, ACC, and ACCpaper of the Maple package MarkovWZ . You can make many more examples on your own, using this package (provided that you have access to Maple, of course!)

Examples of MWZ Identities Whose Kernles Are Powers of the Binomial Coefficients

binomial(n,k): input file output file
binomial(n,k) Squared: input file output file
binomial(n,k) Cubed: input file output file
binomial(n,k) To the Power 4 input file output file
binomial(n,k) To the Power 5: input file output file
binomial(n,k) To the Power 6: input file output file
binomial(n,k) To the Power 7: input file output file
binomial(n,k) To the Power 8: input file output file
binomial(n,k) To the Power 9: input file output file
binomial(n,k) To the Power 10: input file output file
Examples of Convergence-Acceleration Formulas for Zeta(2) Through Zeta(7)

Zeta(2): terse input file terse output file
verbose input file verbose output file
Zeta(3): terse input file terse output file
verbose input file verbose output file
Zeta(4): terse input file terse output file
verbose input file verbose output file
Zeta(5): terse input file terse output file
verbose input file verbose output file
Zeta(6): terse input file terse output file
verbose input file verbose output file
Zeta(7): terse input file terse output file
verbose input file verbose output file
More Sample Input and Output files for MarkovWZ Below you have tersers, additional examples.

To see some `good' kernels for Zeta(2) through Zeta(8), complete with the MWZ pairs and the Acceleration schemes, use input, to get output.
To see the best delta (empirically) with n+k=40, with kernel ((z+x)!/(2*x+z+1)!)^r for appx. Zeta(r) (r between 2 and 6) use input, to get output.
To see the various delta's one gets with various kernles for Zeta(5) use the input, to get output.
To see the best delta (empirically) with n+k=40, with kernel ((z+x)!/(3*x+z+1)!)^r for appx. Zeta(r) (r between 2 and 5), use input, to get output.
To get some best delta's (for cnk's, not the weighted average), for Apery's kernels for log(2), Zeta(2) and Zeta(3), use input, to get output.
To get the MWZ pairs whose kernels are the powers of the binomial coefficients, from the first to the eighth, use input, to get output.
To get some empirical delta's for Apery's appx. seq for Zeta(2) and Zeta(3) (with n+k=20), use input, to get output.
To get some empirical delta's for Apery's appx. seq for Zeta(2) and Zeta(3) (with n+k=40), use input, to get output.
To see the appx. for Zeta(r) (r=2..9) for using ((z+x)!/(2*x+z+1)!)^r, use input, to get output.
To see the appx. for Zeta(r) (r=2..6) for using ((z+x)!/(3*x+z+1)!)^r, use input, to get output.

Doron Zeilberger's List of Papers
Doron Zeilberger's Home Page