Computing infinite series on python

osamie · #1 02-Dec-2008, 11:01

Please I have problem writing a function that returns the cosine of a number with the aid of an infinite series, cos x = 1 − x2⁄2! + x4⁄4! − x6⁄6! + …
The program is meant to collect two arguments; n, number of terms and x, the number.
writing the factorial function wasn't a problem for me. The infinite series one, is just slapping me

Please I need some help

davekw7x · #2 02-Dec-2008, 18:51

Quote:

Originally Posted by osamie

The infinite series one, is just slapping me

I would not actually use the factorial function. My method would be build the terms as you go.

Note that only even-numbered terms of the Taylor series are non-zero

So, for example the sum of first few terms looks like

Code:

sum = 1 - x*x/(2*1) + x*x*x*x/(4*3*2*1)  - x*x*x*x*x*x/(6*5*4*3*2*1)
      ^      ^             ^                         ^
      |      |             |                         |
     i=0    i=2           i=4                       i=6

After the first term, here's the ticket:

The numerator of each term is x*x*(old numerator)
The denominator of the i'th term is i*(i-1)*(old denominator)
The signs of the terms alternate

Here's an approach

Code:

Function that uses N terms to approximate cos(x)
Let num   = 1.0
Let denom = 1.0
Let sum   = 1.0
Let sign  = -1

Let i go from 2 to 2*N in steps of 2
Loop
    Let num = num * x * x
    Let denom = denom * i * (i - 1)
    Let sum = sum + sign * num / denom
    Let sign = -sign
End Loop
return sum

Typical result (for 0.5 radians):

Code:

Approximate value of cos(5.000000e-01) calculated as follows:
 1 term : actual =   8.775826e-01, approx =   1.000000e+00, err =   1.224174e-01
 2 terms: actual =   8.775826e-01, approx =   8.750000e-01, err =  -2.582562e-03
 3 terms: actual =   8.775826e-01, approx =   8.776042e-01, err =   2.160478e-05
 4 terms: actual =   8.775826e-01, approx =   8.775825e-01, err =  -9.661260e-08
 5 terms: actual =   8.775826e-01, approx =   8.775826e-01, err =   2.686054e-10
 6 terms: actual =   8.775826e-01, approx =   8.775826e-01, err =  -5.090373e-13
 7 terms: actual =   8.775826e-01, approx =   8.775826e-01, err =   6.661338e-16

Regards,

Dave

Thread Tools	Search this Thread
Show Printable Version Email this Page	Search this Thread: Advanced Search
Rate This Thread
Rate This Thread:

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Python - Need help with time card script/wage calculator	sigkill9	Python Forum	5	12-Mar-2008 22:01
Neutral Python book - the Quest for the Impossible?	Kimmo	Python Forum	1	04-Aug-2007 13:56
Looking for opinions	crystalattice	Miscellaneous Programming Forum	6	27-Sep-2006 22:02
Re: Beginning Python Tutorial (Part 5)	crystalattice	Python Forum	0	04-Oct-2005 05:27
Re: Beginning Python Tutorial (Part 2)	crystalattice	Python Forum	2	31-Jul-2005 13:25

Computing infinite series on python

Re: Computing ininite series on python