Ahh, I got it!
Problem was that your calculation relied on Mathcad doing implicit vectorization.
You called "disp" and so also "SS" and "PHI" with a vector xi of values but did not explicitly apply vectorization. This worked well with the original formulation of PHI, but failed with the version using sinc becasue here we read sinc(kk*acos(xi) * acos(xi). If xi is a vector, both factors are vectors as well and Mathcad of course will not apply implicit vectorization but rather applies the vector dot product.
Solution is to use vectorization in the definition of function "disp"
OR as an alternative vectorise in the definition of function SS
You don't have to do both but it does no harm if you do.
Another option would be to do the vectorization already in the definition of PHI
Applying vectorisation either way makes you alternative definition of PHI work as well as will my variation of it which I posted above.
These are errors that are not so easy to find and I therefore feel confirmed in my opinion that one should not rely on Mathcad doing implicit vectorisation but rather ALWAYS use explicit vectorization when calling a function written for a scalar argument with a vector as argument and expecting the vector elements to be processed individually.
Here you see the difference between between calling with and without explicit vectorization:
It was my variant of PHI that led me on the right track, because I was initially wondering why “u” was not a vector here, whereas it was a vector in the original variant of PHI and also in your sinc variant (albeit with incorrect values).
MC11 sheet attached
