Special Functions

You can enter the greatest integer function or floor function f (x) = $\left\lfloor\vphantom{ x}\right.$x$\left.\vphantom{ x}\right\rfloor$ by clicking the brackets icon itbpF0.3001in0.3001in0.0701infences.wmf and choosing itbpF0.1989in0.3001in0.0692inlfloor.wmf (see floorDM2-4.tex#Floor).

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$\left\lfloor\vphantom{ x}\right.$x$\left.\vphantom{ x}\right\rfloor$

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In a similar fashion, you can enter the absolute value function f (x) = $\left\vert\vphantom{ x}\right.$x$\left.\vphantom{ x}\right\vert$ by choosing vertical brackets fromitbpF0.3009in0.3009in0.0701inbrackets.wmf. The following shows the graph of f (x) = $\left\vert\vphantom{ \sin x}\right.$sin x$\left.\vphantom{ \sin x}\right\vert$.

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$\left\vert\vphantom{ \sin x}\right.$sin x$\left.\vphantom{ \sin x}\right\vert$

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The Gamma function Γ(x) extends the factorial function in the sense that for each nonnegative integer n the identity Γ(n + 1) = n! holds. The plot of the Gamma function displays the vertical asymptotes with the graph.

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Γ(x)

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The Heaviside function is defined by

H(x) = $\displaystyle \left\{\vphantom{
\begin{array}{ccc}
0 &
\text{if} & x<0 \\
1 & \text{if} & x\geq 0
\end{array}
}\right.$$\displaystyle \begin{array}{ccc}
0 &
\text{if} & x<0 \\
1 & \text{if} & x\geq 0
\end{array}$

You can also call it directly from Maple by choosing Define + Define Maple Name and filling in Heaviside(x) for the Maple Name and H(x) for the Scientific Notebook Name in the dialog box.dtbpF3.0096in3.6936in0ptmapdefin.wmfThe Heaviside function provides an alternative method for creating piecewise-defined functions. Note that H(x - 2)sin(x) + H(- x)cos x is cos x for x≤ 0, sin x for x≥2, and 0 for 0≤x≤2.

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H(x - 2)sin x + H(- x)cos x

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