Secret equation

I got a call this afternoon from someone who records audio books for the blind. He wanted to know the name of a symbol he didn't recognize. He then asked me if the equation was real.

Here's the equation in context, from the book Michael Vey 4: Hunt for Jade Dragon. The context is as follows.

Suddenly math problems she hadn't understood made sense. Except now they weren't just numbers and equations, they were patterns and colors. Calculus, geometry, and trigonometry were easy to understand, simple as a game, like shooting balls at a basketball hoop that was a hundred feet wide. Then a specific sequence of numbers, letters, and symbols started running through her mind.

She almost said the equation when a powerful thought came over her not to speak it out loud-that she must not ever divulge it. She new that what she was receiving was something of great importance, even if she had no idea what it meant.

I believe the symbol in question is the fourth letter of the Hebrew alphabet, a (daleth).

Is this a real equation? The overall form of it looks like an integral transform. However, the two instances of a in equation look suspicious.

One reason is that I've never seen a used in math, though I read somewhere that Cantor used it for the cardinality of some set. Even so, Cantor's use wouldn't make sense inside an integral.

Also, the two instances of a are used differently. The first is a function (or else the factors of 2 I could be cancelled out) and the second one apparently is not. Finally, the equation is symmetric in x and y if you remove the two daleths. So I suspect this was a real equation with the daleths added in for extra mystery.