Symbolics > Working with Symbolics > Calculus > To Expand an Expression into a Taylor or Laurent Series
To Expand an Expression into a Taylor or Laurent Series
1. Place the cursor at the end of a function, insert the symbolic evaluation operator, and type the keyword series in the placeholder.
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The resulting series contains a large number of terms with non-zero coefficients of odd and even powers of x, but PTC Mathcad returns, by default, the first six terms. Specify keyword series,6 and verify that you get the same result.
If the first non-zero term of the series corresponds to xn, then PTC Mathcad returns the terms from xn to xn+k-1.
For the above example, n=0, k=6, and n+k-1=5, and the last displayed term contains x5.
PTC Mathcad does not display terms that have coefficients of 0
2. To return a different number of terms, type a comma after the keyword, followed by a positive integer k.
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The above evaluation calls for returning the expansion terms of the sin function up to the term that contains xn+k-1 or x7, but the result contains four terms only. This is because the terms that contain x0, x2, x4, x6 have coefficients of 0 and thus are not displayed.
3. To expand an expression around a point other than 0, specify a value for the variable after the keyword series, using the Boolean equal operator.
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By default, PTC Mathcad expands the function about point 0.
If the expression contains more than one variable, type a comma after series, and then type a comma-separated list of variables around which you want to expand the series.
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