Raildex

Raildex is the nickname the English-speaking fandom uses for the Toaru Majutsu no Index franchise. It is a portmanteau of Railgun and Index, referring to the animated adaptations.

The Japanese equivalent of this is Toaru (とある), referring to the first three hiragana characters that is now part of the idiosyncratic naming scheme the franchise uses for its series and other properties.

Origin
The first known use of the term "Raildex" was seen in an anonymous post in the /a/ (Anime and Manga) board of 4chan on October 31, 2009, just one day after the 5th episode of Toaru Kagaku no Railgun was first broadcasted. The post was in a thread arguing that Railgun is superior to Index. It was 6th reply in the thread, though the word was never mentioned again before the thread was pruned. Coincidentally, the term Ingun is also used in the post, another fandom term to refer to the franchise, though mostly as a joke.

Spread
The term would later memetically spread the following month in /a/, with no apparent connection to the original "Raildex" post. From then on other anime-related websites with English-speaking communities such as AnimeSuki would use the term as well.

Funimation would later use the term as well, making the term somewhat official.