Ludwig Ritter von Köchel since undergone revisions. Mozart's works are often referred to by their K-numbers ("cf." opus number); for example, the "Jupiter" symphony, "Symphony No. 41" K. 551. Moreover, Köchel arranged Mozart's works into twenty-four categories, which were used by Breitkopf & Härtel when they published the first complete edition of Mozart's works from 1877 to 1910, a venture partly funded by Köchel. He also catalogued the works of Johann Fux. Ludwig Ritter von Köchel Ludwig Alois Friedrich Ritter von Köchel (; 14 January 1800 – 3 June 1877) was an Austrian musicologist, writer, composer, botanist and publisher. He is best known for
Large numbers If we need many such functions we can better number them instead of using a new letter every time, e.g. as a subscript, so we get numbers of the form formula_81 where "k" and "m" are given exactly and n is an integer which may or may not be given exactly. Using "k"=1 for the "f" above, "k"=2 for "g", etc., we have (10→10→"n"→"k") = formula_82. If "n" is large we can use any of the above for expressing it. Thus we get a nesting of forms formula_83 where going inward the "k" decreases, and with as inner argument a