HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 241

hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM REMAINDER TCHEBYCHEFF Note that in step-by-step mode, synthetic division is shown, with each polynomial represented as the list of its coefficients in descending order of power. Returns the remainder from the division of the two polynomials, A(X) and B(X), divided in decreasing order by exponent. Example Typing: REMAINDER(X3 - 1, X2 - 1) gives: x-1 Note that in step-by-step mode, synthetic division is shown, with each polynomial represented as the list of its coefficients in descending order of power. For n > 0, TCHEBYCHEFF returns the polynomial Tn such that: Tn(x) = cos(n·arccos(x)) For n ≥ 0, we have: [ n-- ] ∑ Tn(x) = 2 C2nk(x2 - 1)k xn - 2k k=0 For n ≥ 0 we also have: (1 - x2 ) Tn″ ( x ) - x T ′ n( x ) + n2 Tn ( x ) = 0 For n ≥ 1, we have: Tn + 1(x) = 2xTn(x) - Tn - 1(x) If n < 0, TCHEBYCHEFF returns the 2nd-species Tchebycheff polynomial: Tn(x) = -s--i--sn--i-(-n--n-(---a⋅--r-a-c--r-c-c--o-c--so--(-s--x-(--)x--)--)--) Computer Algebra System (CAS) 14-59