www.FireMath.info

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# Firemath - The Equation Editor

## Example: Taylor expansion

You should start with entering 'sin' into the text field followed by a click onto Func. Now, either click the x button in the common identifiers panel, or insert 'x' into the text field and click onto Identifier. After a click onto the '=' button in the common elements panel, you should have arrived at

$sin⁡ x =$

The next steps consist of clicking onto the sum-operator button in the common elements panel followed by a click onto the fences button . The cursor should now be located within the brackets. Insert '-1' into the text field and click onto Identifier. (Note: Single numbers like '-1' should not be generated by a click onto the minus-operator button followed by inserting '1'.) So far, your equation should look like

$sin⁡ x = ∑ -1$

Move the cursor to the very right and click onto the fraction button . When the cursor is in the nominator, insert an 'x' like described above. Move the cursor into the denominator and insert an 'n' as an identifier. Type an '!' into the text field and click onto the Operator (Op) button. Move the cursor back until it is located on the 'x' in the nominator. Now, click onto the sub-superscript button and place the cursor on the pink dot representing the superscript. Once, you insert an 'n' there, your equation should look like

$sin⁡ x = ∑ -1 x n n !$

We will now add the exponent to expression '(-1)'. For this, place the cursor, such that it extends over the brackets and their content. You can do this either by clicking onto one of the brackets or by moving the cursor. Click onto the sub-superscript button and move the cursor to the superscript. Click onto the fraction button , insert an 'n' into the nominator and a '2' into the denominator. Move the cursor left, until it covers the entire fraction and click onto the attributes button . A new window opens, in which you should set attribute 'Bevelled' to 'True' and click onto OK. The fraction is not enclosed by brackets, yet. Make sure, the cursor still covers the entire fraction and click on any of the fenced buttons while keeping CTRL pressed. The brackets of the fences need to be modified, such that they represent a floor function. For this, locate the cursor such that it covers the brackets and their content. Click onto the attributes button , remove the entries behind 'Open' and 'Close'. Click onto the Symbols buttons of the 'Open' and 'Close' attributes and choose those characters, which make your equation look like

$sin⁡ x = ∑ -1 n 2 x n n !$

What is left is to add the boundaries to the sum operator. Place the cursor onto this operator and click the under- overscript button . The cursor should now be located under the Sigma sign, where we want to insert a two-row entry. The canonical way to do this would be to use an <mtable> element. Unfortunately, Firefox doesn't support the rowspacing attribute, which results in an inappropriate rendering. The trick we apply here is to use a fraction without fraction bar.
Click onto the fraction button and use your knowledge obtained so far, to get 'n=1' into the nominator. Move the cursor into the denominator, insert 'n' as an identifier and click onto the <mspace> button . Type 'odd' into the text field and click onto Text. Move the cursor left, until it covers the entire fraction. Click the attributes button and choose entry '0' from the drop-down menu of the 'Line-Thickness' attribute. Finally, place the cursor on the overscript of the sum operator. After a click onto the button with the infinity sign in the tabs panel you arrive at

$sin⁡ x = ∑ n = 1 n odd ∞ -1 n 2 x n n !$