Complex sentence: The argument\\ scriptstyle of the third kind of integral is known as the characteristic, which in different notational conventions can appear as either the first, second or third argument of\\ scriptstyle, and furthermore is sometimes defined with the opposite sign.
Split into simpler sentences: The argument\\ scriptstyle of the third kind of integral is known as the characteristic, and is the subject of a number of conflicting conventions. The characteristic may appear as either the first, second or third argument of\\ scriptstyle, and furthermore it is sometimes defined with the opposite sign.