long equation do not show up using \[ .. \] but shows up using \begin{align*}...\end{align*}

The formula is built and boxed. However, it exceeds the maximum width by a very large amount and, due to how binary arithmetic works, its width is advertised as -4919.6661pt, whose numeric value is -322415238.

Thus the box is typeset, but nothing can be seen because it is outside the margin of the page.

If you try

\[
\hspace{4919.6661pt}<monster>
\]

you can see the end of the formula.

Why does align show at least some part of the formula? Because it internally uses \halign and not display math mode.

Maybe this could be managed in a different way, but I don't think that it's something to worry about: six meter long formulas are nothing anybody would like to see.

You can make equation look like align but in either case it prints the expression on one line so 99% of it off the page. If you really must print such an expression you need to take more drastic actions to keep it visible. This is visible but of course completely unreadably ugly.

\documentclass[12pt]{article}

\usepackage{amsmath}
\def\WhittakerM{\textrm{WhittakerM}}

\begin{document}

The equation is
\begin{center}
\itshape\footnotesize
\catcode`\^=13
\def^#1{\textsuperscript{(\tiny#1)}}
\def\left{\penalty0 }
\def\right{\penalty0 }
\def\frac#1#2{(#1)
/\penalty0(#2)
\penalty0 }
w 
\left( x,y \right)
 ={\it \_F1} 
\left( {\frac {1}{{b}^{2} 
\left(......
\end{center}

Did you see it?

\end{document}