cachinnate (kak-i-neyt or kak-uh-neyt) v. Latin (cacchinnatus) to laugh loudly and immoderately.
Also cachinnation n. such laughter as described above, and cachinnatory adj. relating to a cachinnation.
From what I can tell, this applies specifically to laughter in situations when the laughter is improper, unwarranted, or in poor taste, not to loud laughter in general. Although, it dates to the mid-nineteenth century when laughter in public was forbidden to proper gentlemen as it was considered unseemly (Presumably also ladies? but I only saw men referenced).
Although I know it to be impious, I cannot help but cachinnate during the church service each time the pastor says 'sects.'
The class waited in anticipation as Ms. Smith sat down at her desk only to erupt in cachinnations when the whoopie cushion placed there emitted its trademark sound.