0,3

Discriminant of Chebyshev polynomial T_n (x) of first kind.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795.

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

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Index entries for sequences related to Chebyshev polynomials.

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

a(n) = ((2^((n-1)^2))*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((2*i-1)*Pi/(2*n)), i=1,..,n, are the zeros of the Chebyshev T(n,x) polynomials.

a(n) = ((-1)^(n*(n-1)/2))*(2^((n-1)*(n-2))) * product(diff(T(n,x),x)|_{x=xn[i]},i=1..n), n>0, with the zeros xn[i],i=1..n, given above.

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

(PARI) a(n)=if(n<1, 0, poldisc(poltchebi(n)))

Cf. A086804.

Cf. A127670 (discriminant for S-polynomials).

Sequence in context: A038782 A024110 A132099 this_sequence A101356 A069442 A013457

Adjacent sequences: A007698 A007699 A007700 this_sequence A007702 A007703 A007704

nonn

N. J. A. Sloane (njas(AT)research.att.com).

Additional comments from Michael Somos, Jun 26, 2002