HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 195

The TCHEBYCHEFF function The function TCHEBYCHEFF(n) generates the Tchebycheff (or Chebyshev) polynomial of the first kind, order n, defined as Tn(X) = cos(n⋅arccos(X)). If the integer n is negative (n < 0), the function TCHEBYCHEFF(n) generates the Tchebycheff polynomial of the second kind, order n, defined as Tn(X) = sin(n⋅arccos(X))/sin(arccos(X)). Examples: TCHEBYCHEFF(3) = 4*X^3-3*X TCHEBYCHEFF(-3) = 4*X^2-1 Fractions Fractions can be expanded and factored by using functions EXPAND and FACTOR, from the ALG menu (,×). For example: EXPAND('(1+X)^3/((X-1)(X+3))') = '(X^3+3*X^2+3*X+1)/(X^2+2*X-3)' EXPAND('(X^2*(X+Y)/(2*X-X^2)^2') = '(X+Y)/(X^2-4*X+4)' EXPAND('X*(X+Y)/(X^2-1)') = '(X^2+Y*X)/(X^2-1)' EXPAND('4+2*(X-1)+3/((X-2)*(X+3))-5/X^2') = '(2*X^5+4*X^4-10*X^3-14*X^2-5*X)/(X^4+X^3-6*X^2)' FACTOR('(3*X^3-2*X^2)/(X^2-5*X+6)') = 'X^2*(3*X-2)/((X-2)*(X-3))' FACTOR('(X^3-9*X)/(X^2-5*X+6)' ) = 'X*(X+3)/(X-2)' FACTOR('(X^2-1)/(X^3*Y-Y)') = '(X+1)/((X^2+X+1)*Y)' The SIMP2 function Functions SIMP2 and PROPFRAC are used to simplify a fraction and to produce a proper fraction, respectively. Function SIMP2 takes as arguments two numbers or polynomials, representing the numerator and denominator of a rational fraction, and returns the simplified numerator and denominator. For example: SIMP2('X^3-1','X^2-4*X+3') = { 'X^2+X+1','X-3'}. The PROPFRAC function The function PROPFRAC converts a rational fraction into a "proper" fraction, i.e., an integer part added to a fractional part, if such decomposition is possible. For example: Page 5-24