0,3

Discriminant of Chebyshev polynomial U_n (x) of second kind.

Theodore J. Rivlin, Chebyshev polynomials: from approximation theory to algebra and number theory, 2. ed., Wiley, New York, 1990; p. 219, 5.1.2.

Index entries for sequences related to Chebyshev polynomials.

a(n)=((n+1)^(n-2))*2^(n^2), n>=1, a(0):=0.

a(n)=((2^(2*(n-1)))*Det(Vn(xn[1],..,xn[n])))^2, n>=1, with the determinant of the Vandermonde matrix Vn with elements (Vn)i,j:= xn[i]^j, i=1..n,j=0..n-1, and xn[i]:=cos(Pi*i/(n+1)), i=1,..,n, are the zeros of the Chebyshev U(n,x) polynomials.

a(n)= ((-1)^(n*(n-1)/2))*(2^(n*(n-2)))*product(diff(U(n,x),x)|_{x=xn[i]},i=1..n)), n>=1, with the zeros xn[i],i=1..n, given above.

(PARI) a(n)=if(n<1, 0, (n+1)^(n-2)*2^(n^2))

(PARI) a(n)=if(n<1, 0, n++; poldisc(poltchebi(n)'/n))

Cf. A007701.

Cf. A127670 (discriminant for S-polynomials).

Sequence in context: A054947 A071900 A075413 this_sequence A121366 A065776 A101800

Adjacent sequences: A086801 A086802 A086803 this_sequence A086805 A086806 A086807

nonn

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 05 2003

Formula and more terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 07 2003