HP 40gs User Manual page 241

hp40g+.book Page 59 Friday, December 9, 2005 1:03 AM
REMAINDER
TCHEBYCHEFF
Computer Algebra System (CAS)
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:
3
REMAINDER(X – 1, X
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 T
that:
Tn(x) = cos(n·arccos(x))
For n ≥ 0, we have:
n
[ ]
-- -
2
2
2k
∑
x ( ) (
T = C x –
n
n
k = 0
For n ≥ 0 we also have:
'
)T " n x ( ) xT
2
( n x ( )
1 x – –
For n ≥ 1, we have:
x ( ) x ( ) T
T = 2xT –
n + 1 n
If n < 0, TCHEBYCHEFF returns the 2nd-species
Tchebycheff polynomial:
( n arccos x ( ) ⋅
sin
x ( ) ------------------------------------------ -
T =
n ( arccos x ( )
sin
2
– 1)
k
n 2 k –
)
1 x
2
x ( )
+ n T = 0
n
x ( )
n 1 –
)
)
such
n
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