Terms in series expansion

[Gaurav Sathe]

I'm a little confused with the .series method. 

In [8]: sin(x).series(x,0,10)

Out[8]:

        3        5         7             9             

      x        x         x             x              

x - ── + ─── - ──── + ────── + O(x**10)

      6      120     5040       362880           

In [9]: cos(x).series(x,0,10)

Out[9]: 

        2       4       6           8            

      x       x       x           x             

1 - ── + ── - ─── + ───── + O(x**10)

      2      24    720      40320           

From this it seems that .series(x,point,n) calculates the series expansion of f(x) till the nth exponent of x...

But,

In [17]: exp(x**2).series(x,0,10)

Out[17]: 

                4       6       8        10      12         14          16             18             

        2    x       x       x        x        x           x            x              x               

1 + x  + ── + ── + ── + ─── + ─── + ──── + ───── + ────── + O(x**20)

              2       6     24      120     720      5040       40320      362880           

This doesnt seem to match up... Does the parameter 'n' mean 'the no of terms in the series expansion' or ' the last exponent of x in the expansion'  ?

 

[Sai Nikhil]

parameter 'n' was written to imply last exponent of 'x' in the expansion, I guess

but, in second case, exp(x**2) = exp(v), where v = x**2 and so, exp(v) is calculated till, v**9 and substituting, v=x**2, we are getting the above result.

this is obviously supposed to be an issue, and if Mr.Aaron permits, I'll try to submit a suitable patch for this ...

-thanks ,

Sai Nikhil.T

1

[Rhythm Gupta]

Hi, I think it this way,
If you will use
f(m).series(x,0,n) , where m is a function of x.
then it will return the series till the nth power of m.(#not x)

On Wed, Mar 14, 2012 at 7:34 PM, Gaurav Sathe <gaurav....@gmail.com> wrote:

I'm a little confused with the .series method. 

In [8]: sin(x).series(x,0,10)

Out[8]:

        3        5         7             9             

      x        x         x             x              

x - ── + ─── - ──── + ────── + O(x**10)

      6      120     5040       362880           

 

In [9]: cos(x).series(x,0,10)

Out[9]: 

        2       4       6           8            

      x       x       x           x             

1 - ── + ── - ─── + ───── + O(x**10)

      2      24    720      40320           

From this it seems that .series(x,point,n) calculates the series expansion of f(x) till the nth exponent of x...

In both of the above cases, x==m.Hence it appears that it calculates the series expansion of f(x) till the nth exponent of x.

 

But,

In [17]: exp(x**2).series(x,0,10)

Out[17]: 

                4       6       8        10      12         14          16             18             

        2    x       x       x        x        x           x            x              x               

1 + x  + ── + ── + ── + ─── + ─── + ──── + ───── + ────── + O(x**20)

              2       6     24      120     720      5040       40320      362880           

This doesnt seem to match up... Does the parameter 'n' mean 'the no of terms in the series expansion' or ' the last exponent of x in the expansion'  ?

 

Thanks
Rhythm Gupta
 

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[krastano...@gmail.com]

Is this in the current master branch or an old version?

I get this:
In [1]: exp(x**2).series(x,0,10)
Out[1]:

4 6 8
2 x x x ⎛ 10⎞
1 + x + ── + ── + ── + O⎝x ⎠
2 6 24

And it seems correct.

[Gaurav Sathe]

Thnx... I was thinking of the same logic which u have said... but then how do we explain the below series expansion:

>>> (sin(x)/x**10).series(x,0,10)

   1                   1        1            1                1          

──────── + ── - ──── + ────── - ─────── + O(1)

362880⋅x            9         7               5               3       

                       x      6⋅x         120⋅x        5040⋅x        

Do we say that it is like dividing each term of the sin(x) series by x**10 ?

-Gaurav

 

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--
Gaurav Sathe
-Student at BITS Pilani - Goa Campus

[Rhythm Gupta]

I think Yes.

[krastano...@gmail.com]

Again, this is not what I get in the current master branch:

In [1]: (sin(x)/x**10).series(x,0,10)
Out[1]:

3 5
1 1 1 1 1 x x x
── - ──── + ────── - ─────── + ──────── - ──────── + ────────── - ────────────
9 7 5 3 362880⋅x 39916800 6227020800 130767436800

x 6⋅x 120⋅x 5040⋅x

7 9
x x ⎛ 10⎞
─ + ─────────────── - ────────────────── + O⎝x ⎠
0 355687428096000 121645100408832000

It works as expected. Can you check which version of sympy you are
actually using? Is it the master branch or a released version?