Insert name underneath equation

Question

I have this code

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=2.5cm,showframe]{geometry}
\usepackage{amsmath}

\begin{document}

\begin{equation}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation}

\end{document}

which produces this output

Is there a way to give the equation a name, f.x. Itô's Lemma, and insert it directly underneath the equation (centered)? The idea is that it is still a part of the \begin{equation}...\end{equation} environment. I have read this, but the solution is not exactly the same. Thanks in advance!

Answer 1

It doesn't seem like a good idea, but the document is yours. The approach in the linked question is much worse, however.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=2.5cm,showframe]{geometry}
\usepackage{amsmath}

\begin{document}

\begin{gather}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\\
\text{Itô's lemma}\notag
\end{gather}

\end{document}

For completeness, I'd rather go with something like below.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=2.5cm,showframe]{geometry}
\usepackage{amsmath}

\begin{document}

We obtain the following equation, known as \emph{Itô's lemma},
\begin{equation}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation}

\end{document}

In the case you seem to be after, I can suggest something like this.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=2.5cm,showframe]{geometry}
\usepackage{amsmath}
\usepackage{nccmath}

\begin{document}

\section{Main body}

We recall the fundamental \emph{Pythagoras' theorem}
\begin{equation}\label{pyth}
a^2+b^2=c^2
\end{equation}
From it we easily obtain the following equation, known as \emph{Itô's lemma},
\begin{equation}\label{ito}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation}

\begin{fleqn}[2em]
\setlength{\parindent}{0pt}

\section{Equations}

Pythagoras' theorem
\begin{equation}\tag{\ref{pyth}}
a^2+b^2=c^2
\end{equation}

Itô's lemma
\begin{equation}\tag{\ref{ito}}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation}

\end{fleqn}

\end{document}

Alternatively, with the references next to the name:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=2.5cm,showframe]{geometry}
\usepackage{amsmath}
\usepackage{nccmath}

\begin{document}

\section{Main body}

We recall the fundamental \emph{Pythagoras' theorem}
\begin{equation}\label{pyth}
a^2+b^2=c^2
\end{equation}
From it we easily obtain the following equation, known as \emph{Itô's lemma},
\begin{equation}\label{ito}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation}

\begin{fleqn}[2em]
\setlength{\parindent}{0pt}

\section{Equations}

Pythagoras' theorem~\eqref{pyth}
\begin{equation*}
a^2+b^2=c^2
\end{equation*}

Itô's lemma~\eqref{ito}
\begin{equation*}
    dy_{t}
        =\frac{\partial g}{\partial t}(x_{t},t)dt
        +\frac{\partial g}{\partial x}(x_{t},t)dx_{t}
        +\frac{1}{2}\frac{\partial^2 g}{\partial x^2}(x_{t},t)(dx_{t})^2
\end{equation*}

\end{fleqn}

\end{document}