Previous Page Next Page Contents

ORDER -- the default number of terms in series expansions

Introduction

The environment variable ORDER controls the default number of terms that the system returns when you compute a series expansion.

Call(s)


ORDER
ORDER := n

Parameters

n - a positive integer less than 2^31. The default value is 6.

Related Functions

asympt, limit, O, series, taylor

Details

Example 1

In the following example, we compute the first 6 terms of the series expansion of the exponential function around the origin:

>> series(exp(x), x = 0)
                             2    3    4    5
                            x    x    x    x        6
                    1 + x + -- + -- + -- + --- + O(x )
                            2    6    24   120

To obtain the first 10 terms, we specify the third argument of series:

>> series(exp(x), x = 0, 10)
               2    3    4    5     6      7      8        9
              x    x    x    x     x      x      x        x
      1 + x + -- + -- + -- + --- + --- + ---- + ----- + ------ +
              2    6    24   120   720   5040   40320   362880
      
            10
         O(x  )

Alternatively, we increase the value of ORDER. This affects all subsequent calls to series or any other function returning a series expansion:

>> ORDER := 10: series(exp(x), x = 0)
               2    3    4    5     6      7      8        9
              x    x    x    x     x      x      x        x
      1 + x + -- + -- + -- + --- + --- + ---- + ----- + ------ +
              2    6    24   120   720   5040   40320   362880
      
            10
         O(x  )
>> taylor(x^2/(1 - x), x = 0)
         2    3    4    5    6    7    8    9    10    11      12
        x  + x  + x  + x  + x  + x  + x  + x  + x   + x   + O(x  )

Finally, we reset ORDER to its default value 6:

>> delete ORDER: taylor(x^2/(1 - x), x = 0)
                     2    3    4    5    6    7      8
                    x  + x  + x  + x  + x  + x  + O(x )

Example 2

Here are some examples where the number of terms returned by series differs from the value of ORDER:

>> ORDER := 3:
>> series((x^2 + x)^2, x = 0)
                                 2      3
                                x  + O(x )
>> series(exp(x) - 1 - x, x = 0)
                                 2
                                x       3
                                -- + O(x )
                                2
>> series(1/(1 - sqrt(x)), x = 0)
                         1/2        3/2    2      5/2
                    1 + x    + x + x    + x  + O(x   )
>> delete ORDER: 

Changes




Do you have questions or comments?


Copyright © SciFace Software GmbH & Co. KG 2000