The lcm function, The legendre function, The lcm function ,5-20 the legendre function ,5-20 – HP 50g Graphing Calculator User Manual

Page 197

Advertising
background image

Page 5-20

For example, for n = 2, we will write:

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)’.

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.,

LEGENDRE(3) = ‘(5*X^3-3*X)/2’

LEGENDRE(5) = ‘(63*X ^5-70*X^3+15*X)/8’

Note: Matrices are introduced in Chapter 10.

.

)

(

)

(

)

(

1

,

1

,

1

1

j

n

j

n

j

k

k

k

j

n

j

k

k

k

n

y

x

x

x

x

x

p

=

=

=

=

2

1

2

1

1

2

2

1

2

1

2

1

1

2

1

2

1

)

(

)

(

)

(

x

x

x

y

x

y

x

y

y

y

x

x

x

x

y

x

x

x

x

x

p

+

=

+

=

0

)

1

(

2

)

1

(

2

2

2

=

+

+

y

n

n

dx

dy

x

dx

y

d

x

Advertising