@MikeS Your code does not work because you have MATRIX. It should be Matrix.l

Please provide an example of what you mean.

@Kitonum There's a difference between matrices being identical and them having equal entries. If you test is(A=A1), the result is false. Equal only checks that the entries are equal.

@Erfan You have misspelled the command name. It's KroneckerProduct, not KroneckeProduct.

@Hulalarip To get more information about that, you'll need to post your system of equations.

You intend to use the C variables as symbolic names, right? rather than assigning them values?

If m and m' both range from 1 to N, then m'' = m-m' will be zero or negative for many pairs (m,m'). Yet m'' is one of your function indices. How do you handle that?

You wrote, "Sketch, on the same plane, the curve...." But the curve does not lie in any plane. The curve is a helix on an elliptic cylinder around the x-axis.

Update: Perhaps "same plane" is meant as "same graph" because any 3-D graph can be considered to be lying in the plane of the paper or screen on which it is drawn.

You have a typo. The equation of the circular cylinder should be x^2 + y^2 = a^2. You have x^2+y^3^=a^2.

@Aakanksha 

What's the point of summing 1000 terms when you don't have numeric values for Xi and gamma[o]? You'll just get an expression with 1000 terms.

What is the parameter Xi? What is gamma[o]?

@acer 

Better yet,

plots:-display(plot([[0,0]], color= white), plots:-pointplot( DataTable3 ));

@nama 

The possibility of equality is always part of the null hypothesis and never part of the alternative hypothesis.

@nama 

The command

Statistics:-TwoSamplePairedTTest(X, Z, 0, confidence= 0.95, alternative= 'lowertail')

means that the alternative hypothesis is that the first factor (X) is less than the second factor (Z).

What input did you call the procedure with?

Please either post the procedure as plaintext so that I can cut and paste it or attach it as a worksheet so that I can download it.