Search code examples
maxima

Maxima - what returns a function chebyshev_t(n, t)

I have probably a very simple question.

What returns in Maxima function chebyshev_t(n, t)? I mean the exact mathematical formula.

Best Regards

Solution

  • When n is a literal integer (e.g. 2, 3, 5, etc) then chebyshev_t evaluates to a polynomial.

    When n is a symbol declared an integer (via declare(n, integer) then chebyshev_t evaluates to a summation.

    (%i1) display2d : false $
(%i2) chebyshev_t (5, u);
(%o2) -25*(1-u)-16*(1-u)^5+80*(1-u)^4-140*(1-u)^3+100*(1-u)^2+1
(%i3) declare (m, integer);
(%o3) done
(%i4) chebyshev_t (m, u);
(%o4) 'sum(pochhammer(-m,i1)*pochhammer(m,i1)*(1-u)^i1
            /(pochhammer(1/2,i1)*2^i1*i1!),i1,0,m)