How can I define a new operator, which works the same as sum, prod in both inline and display math mode?

Question

I want to define a new operator say \Delta . Which works as the same as \sum or \prod in both in line and display math mode. Say, the subscribes is to the right of the operator in the in line mode, and under the operator in the display mode. How can we do this?

Answer 1

If you want it to be literally the size of \sum, then this twist will scale the \Delta to match the vertical footprint of \sum.

\documentclass{article}
\usepackage{amsmath,scalerel}
\DeclareMathOperator*{\Del}{\scalerel*{\Delta}{\sum}}
\begin{document}
  $\Del_{i=0}^n x_i=0$
  \[\Del_{i=0}^n x_i=0\]
\end{document}

Answer 2

You can do it with \DeclareMathOperator* provided by amsmath. Refer to amsmath manual, page 17 for more details.

\documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\Del}{\Delta}
\begin{document}
  $\Del_x^y=0$
  \[\Del_x^y=0\]
\end{document}