sigma above and below in math mode latex

Lussy04

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22-01-2025

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Sigma notation, or summation notation, is a concise way to represent the sum of a series of terms. In LaTeX's math mode, you can easily create sigma notation with limits (both above and below) to clearly express the starting and ending points of your summation. This guide will show you how.

Basic Sigma Notation

The simplest form uses the \sum command:

\sum_{i=1}^{n} i

This renders as: ∑_i=1ⁿ i

This represents the sum of integers from 1 to n. The i=1 is the lower limit (the starting value of the index), and n is the upper limit (the ending value).

Customizing Limits: Placement and Style

You can customize the placement and appearance of your summation limits. Sometimes, especially with complex expressions, the default placement might look cramped. Here are some ways to adjust:

\limits and \nolimits

• \limits: Forces the limits to be placed above and below the summation symbol, regardless of the display style (inline or display math).

• \nolimits: Forces the limits to be placed to the right of the summation symbol, typically used in inline mode to avoid overly large expressions.

Example:

\sum\limits_{i=1}^{n} i^2 \qquad \sum_{i=1}^{n} i^2

This produces: ∑_i=1ⁿ i² and ∑_i=1ⁿ i² (notice the difference in the inline version)

Adjusting Size and Spacing

If your limits are very long expressions, you might need additional adjustments for better readability. You could:

• Use \displaystyle: This command ensures that the summation is displayed in a larger size, making the limits easier to read, particularly useful within an inline equation.

• Add spacing: Employ commands like \, (thin space), \; (medium space), or \quad (large space) to add extra horizontal space between the summation symbol and the limits if needed.

Example:

\sum\limits_{i=1}^{n^2} i \qquad \sum\limits_{i=1}^{\text{a very long expression}} i

The second example may benefit from adding some spaces between the sigma and the upper limit for better readability.

Multiple Summations

You can nest multiple summations:

\sum_{i=1}^{n} \sum_{j=1}^{m} i \cdot j

This renders as: ∑_i=1ⁿ ∑_j=1^m i ⋅ j

Other Summation Symbols

LaTeX supports various summation symbols beyond the basic sigma:

• Product: \prod (∏) for representing products.
• Intersection: \bigcap (∩) for set intersections.
• Union: \bigcup (∪) for set unions.

These all work similarly to \sum, allowing you to specify limits above and below.

Example: A Complete Example with Styling

Let's create a more complex example illustrating different styling options:

\begin{equation}
\sum\limits_{i=1}^{N} \sum\limits_{j=1}^{M} \frac{i}{j^2 + 1} = \sum\limits_{i=1}^{\infty} \frac{1}{i^2}
\end{equation}

This provides a clear and well-formatted equation, demonstrating the power and flexibility of LaTeX's math mode for expressing summations. Remember to compile your LaTeX code to see the rendered output. The output will be a nicely formatted equation with clearly defined limits above and below the summation symbols.

By understanding these techniques, you can effectively and elegantly represent sigma notation with limits (above and below) in your LaTeX documents for clear and professional mathematical expressions. Remember to experiment with different commands to find the most visually appealing and readable style for your specific needs.