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9.4.4 Functional Names

Functions such as log and tan can't simply be typed in as log or tan otherwise they will come out looking like the variables l times o times g ( l o g ) or t times a times n ( t a n ). Instead you should use one of the commands listed in Table 9.5. The functions denoted with can have limits by using the subscript command _ or the superscript command ^[Sub- and superscript positioning for operators]. In addition, the modulo commands listed in Table 9.6 are also available.

Table 9.5: Function Names ( indicates command may have limits, defined by amsmath).
\arccos $ \arccos$ \arcsin $ \arcsin$ \arctan $ \arctan$
\arg $ \arg$ \cos $ \cos$ \cosh $ \cosh$
\cot $ \cot$ \coth $ \coth$ \csc $ \csc$
\deg $ \deg$ \det $ \det$ \dim $ \dim$
\exp $ \exp$ \gcd $ \gcd$ \hom $ \hom$
\inf $ \inf$ \injlim†‡ $ \injlim$ \ker $ \ker$
\lg $ \lg$ \lim $ \lim$ \liminf $ \liminf$
\limsup $ \limsup$ \ln $ \ln$ \log $ \log$
\max $ \max$ \min $ \min$ \Pr $ \Pr$
\projlim†‡ $ \projlim$ \sec $ \sec$ \sin $ \sin$
\sinh $ \sinh$ \sup $ \sup$ \tan $ \tan$
\tanh $ \tanh$ \varinjlim†‡ $ \varinjlim$ \varliminf†‡ $ \varliminf$
\varlimsup†‡ $ \varlimsup$ \varprojlim†‡ $ \varprojlim$    

Table 9.6: Modulo Commands ( defined by amsmath package)
Command Example Input Example Output
\bmod $m \bmod n$ $ m \bmod n$
\pmod{<maths>} $m \pmod{n}$ $ m \pmod{n}$
\mod{<maths>} $m \mod{n}$ $ m \mod{n}$
\pod{<maths>} $m \pod{n}$ $ m \pod{n}$

Example (Trigonometric Functions):

This example uses the cos and sin functions and also the Greek letter theta.

\[ z = r(\cos\theta + i\sin\theta) \]

Image: z equals r (cos theta plus i sign theta)

Example (Limit):

The command \infty is the infinity symbol image of infinity symbol , and the command \to displays an arrow pointing to the right. Note the use of _ since the limit is a subscript.

\[ \lim_{x\to\infty} f(x) \]

Image: limit as x tends to infinity of f of x

The operators with limits behave differently depending on whether they are in displayed or in-line maths. Notice the difference when the same code appears in-line:

In a line of text $\lim_{x\to\infty} f(x)$

which now displays as:

Image: the limit appears to the side of lim instead
of below it.

Example (With Subscript):

This is another example of a functional name using a subscript:

\[ \min_x f(x) \]

Image: the x appears below the word min.

Again, notice the difference when it is used in-line:

In a line of text $\min_x f(x)$

Image: the x appears to the side of the word min. Defining New Functional Operators

It may be that you want a function that isn't specified in Table 9.5. In this case, the amsmath provides the preamble only command

\DeclareMathOperator{<cmd>}{<operator name>}

or its starred variant

\DeclareMathOperator*{<cmd>}{<operator name>}

[Defining a new log-like function in LaTeX]Both versions define a command called <cmd>, which must start with a backslash, that typesets <operator name> as a function name. The starred version is for function names that can take limits (like \lim and \min described above).

Example (Operator Without Limits):

Suppose I want a function called card, which represents the cardinality of a set $ \mathcal{S}$ . First I need to define the new operator command (which I'm going to call \card) in the preamble:


This operator doesn't take any limits, so I have used the unstarred version.

Later in the document, I can use this new operator command:

\[ n = \card(\mathcal{S}) \]

Image: n equals card (S)

In this example \mathcal is used as sets are typically represented in a calligraphic font.

Example (Operator With Limits):

Suppose I now want a function called mode, which represents the mode of a set of numbers. First, I define the operator command in the preamble:


This operator needs to be able to have a subscript, so I have used the starred version.

Later in the document, I can use this new operator command:

\[ x_m = \mode_{x \in \mathcal{S}}(x) \]

Image: x subscript m equals mode of x in S of x

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