I need the LaTeX equation with double square bracket and double paranthesis. Can anyone suggest me the proper code? Here, I had attached the screenshots.

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6
In favour of Consistent typography, I always suggest creating a command that generates a certain output:

\documentclass{article}
\newcommand{\llrrbracket}[1]{% \llrrbracket{..}
\left[\mkern-3mu\left[#1\right]\mkern-3mu\right]}
\newcommand{\llrrparen}[1]{% \llrrparen{..}
\left(\mkern-6mu\left(#1\right)\mkern-6mu\right)}
\begin{document}
\[
\llrrbracket{\frac{1}{x}} \quad \mbox{in the case }
P_\infty = F_p\llrrparen{\frac{1}{x}}
\]
\end{document}
You can, of course, play around with the choice of \mkern, which brings the two elements together.
Werner
- 603,163
5
You can try the following:
\documentclass{article}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{stmaryrd}
\begin{document}
\begin{equation}
\bigg\llbracket \frac{1}{x}\bigg\rrbracket \text{ in the case } P_\infty = \mathbb{F}_p \left(\left(\frac{1}{x} \right)\right)
\end{equation}
\end{document}

EDIT:
I have updated the code to contain the suggestion given in the comment. The above code uses the stmaryrd package.
stmaryrdpackage has\llbracketand\rrbracketwhich would cover your first example. See http://www.tex.ac.uk/tex-archive/info/symbols/comprehensive/symbols-a4.pdf – Steven B. Segletes Jul 31 '13 at 22:38