HP 50g User Manual page 197

For example, for n = 2, we will write:
x
p ( x )
1
x
1
Check this result with your calculator:
LAGRANGE([[ x1,x2],[y1,y2]]) = '((y1-y2)*X+(y2*x1-y1*x2))/(x1-x2)'.
Other examples: LAGRANGE([[1, 2, 3][2, 8, 15]]) = '(X^2+9*X-6)/2'
LAGRANGE([[0.5,1.5,2.5,3.5,4.5][12.2,13.5,19.2,27.3,32.5]]) =
'-(.1375*X^4+ -.7666666666667*X^3+ - .74375*X^2 +
1.991666666667*X-12.92265625)'.
Note: Matrices are introduced in Chapter 10.
The LCM function
The function LCM (Least Common Multiple) obtains the least common multiple
of two polynomials or of lists of polynomials of the same length. Examples:
LCM('2*X^2+4*X+2' ,'X^2-1' ) = '(2*X^2+4*X+2)*(X-1)'.
LCM('X^3-1','X^2+2*X') = '(X^3-1)*( X^2+2*X)'
The LEGENDRE function
A Legendre polynomial of order n is a polynomial function that solves the
differential equation
To obtain the n-th order Legendre polynomial, use LEGENDRE(n), e.g.,
p ( x )
n 1
x x
2 y
1
x x
2 2
d
2
1 ( )
x
dx
LEGENDRE(3) = '(5*X^3-3*X)/2'
LEGENDRE(5) = '(63*X ^5-70*X^3+15*X)/8'
n
( x x
n
∑
k , 1 k j
n
( x
j 1
j
k , 1 k j
x ( y
1 y 1
2
x
1
2
y dy
2
x
2
dx
)
k
y .
j
x )
k
y ) x ( y x
2 2 1
x x
1 2
( ) 1
n n y
y x )
1 2
0
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