HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 191

The HERMITE function The function HERMITE [HERMI] uses as argument an integer number, k, and returns the Hermite polynomial of k-th degree. A Hermite polynomial, Hek(x) is defined as He0 = 1, Hen (x) = (−1)n ex2 /2 dn dxn (e− x 2 / 2 ), n = 1,2,... An alternate definition of the Hermite polynomials is H0* = 1, Hn * (x) = (−1)n ex2 dn dxn (e− x2 ), n = 1,2,... where dn/dxn = n-th derivative with respect to x. This is the definition used in the calculator. Examples: The Hermite polynomials of orders 3 and 5 are given by: HERMITE(3) = '8*X^3-12*X' , And HERMITE(5) = '32*x^5-160*X^3+120*X'. The HORNER function The function HORNER produces the Horner division, or synthetic division, of a polynomial P(X) by the factor (X-a). The input to the function are the polynomial P(X) and the number a. The function returns the quotient polynomial Q(X) that results from dividing P(X) by (X-a), the value of a, and the value of P(a), in that order. In other words, P(X) = Q(X)(X-a)+P(a). For example, HORNER('X^3+2*X^2-3*X+1',2) = {'X^2+4*X+5', 2, 11}. We could, therefore, write X3+2X2-3X+1 = (X2+4X+5)(X-2)+11. A second example: HORNER('X^6-1',-5)= {'X^5-5*X^4+25*X^3-125*X^2+625*X-3125',-5, 15624} i.e., X6-1 = (X5-5*X4+25X3-125X2+625X-3125)(X+5)+15624. The variable VX A variable called VX exists in the calculator's {HOME CASDIR} directory that takes, by default, the value of 'X'. This is the name of the preferred independent variable for algebraic and calculus applications. Avoid using the variable VX in your programs or equations, so as to not get it confused with the CAS' VX. If you need to refer to the x-component of velocity, for example, you can use vx or Vx. For additional information on the CAS variable see Appendix C. Page 5-20