Editing Clenshaw algorithm (section)

===Special case for Chebyshev series===
Consider a truncated [[Chebyshev series]]
<math display="block">p_n(x) = a_0 + a_1 T_1(x) + a_2 T_2(x) + \cdots + a_n T_n(x).</math>

The coefficients in the recursion relation for the [[Chebyshev polynomials]] are
<math display="block">\alpha(x) = 2x, \quad \beta = -1,</math>
with the initial conditions
<math display="block">T_0(x) = 1, \quad T_1(x) = x.</math>

Thus, the recurrence is
<math display="block">b_k(x) = a_k + 2xb_{k+1}(x) - b_{k+2}(x)</math>
and the final results are
<math display="block">b_0(x) = a_0 + 2xb_1(x) - b_2(x),</math>
<math display="block">p_n(x) = \tfrac{1}{2} \left[a_0+b_0(x) - b_2(x)\right].</math>

An equivalent expression for the sum is given by
<math display="block">p_n(x) = a_0 + xb_1(x) - b_2(x).</math>