Im just wandering what is the longest equation in mathematics?
This statement is a bit misleading, acutally many "equations" are truncations of the infinite series. It would make no sense to create an infinite series of something which did not start that way. The common practise is to make a small angle, or similar, approximaition by ignoring all non linear terms of an infinite series. One simply does not arbitaraly ADD non linear terms as this question would seem to imply.Originally posted by quartodeciman
An associated question might be:
What is the longest complete formula that is of true interest to the math sciences, and not just an expansion of something shorter.
What point are you contesting? The fact that many common equations are linear forms of nonliner solutions?Originally posted by quartodeciman
Please permit me to contest your point. First order equations are fine if you want to express a simplified case of something, but may be insufficient for a more detailed explanation. I intended for a closed formula to include terms of real interest, and to avoid arbitrary extensions of series'. Such series' terms express higher order moments and the like.
A real problem with this type of question is the fact that more and more special function names get added to the approved list, which permits shortened expression. It was common to use truncated series throughout the eighteenth century for things that were subsequently given designations and symbolic names, like Bessel, Legendre, etc. in the nineteenth century. The best case of an otherwise-longish formula is Einstein's Gik-Tik gravitational field equation. Write it out with derivatives and products of the metric tensor terms (gik), along with the determinate g, and the formula gets rather long, not to mention boringly repetitious.
I would guess einsteinian77 asked just out of sheer curiosity, which is probably the best motivation you could ask for in these forums.Tell me, please, what will you do with the world's longest formula-that-isn't-just-some-expansions-of-functions-by-series'-terms, once you figure out what it might be?