hp40g+.book Page 18 Friday, December 9, 2005 1:03 AM

and with period T (T being equal to the contents of the variable PERIOD).

If f(x) is a discrete series, then:

+

∞

2iNxπ

 

---------------

f(x) = ∑ cNe

T

N= –∞

Example

Determine the Fourier coefficients of a periodic function f with period 2π and defined over interval [0, 2π] by

f(x)=x2.

Typing:

STORE(2π,PERIOD)

FOURIER(X2,N)

The calculator does not know that N is a whole number, so you have to replace EXP(2∗ i∗N∗π) with 1 and then simplify the expression. We get

 

2 ⋅ i ⋅ N ⋅ π + 2

 

----------------------------------

 

 

N2

 

So if N ≠ 0 , then:

 

cN = 2---------------------------------⋅i ⋅ N ⋅ π + 2-

 

 

 

N2

 

Typing:

 

 

 

FOURIER(X2,0)

 

gives:

 

 

 

4 ⋅ π2

 

 

 

------------

 

 

 

3

 

 

 

so if N = 0 , then:

 

c0 =

4 ⋅ π2

 

------------

3

IBP

Partial integration

 

IBP has two parameters: an expression of the form

 

u(x) ⋅ v'(x)

and v(x) .

14-18

 

 

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