Recently, I submitted for publication to a peer-reviewed math journal
a formula for the n-th order implicit derivative given an implicit function G(z,w)=0.
i.e. dz/dw = - Gw/Gz where Gw and Gz are partial derivatives of G with respect to w and z, respectively. Anyway, I proved the general formula for d^n z/ dw^n. I have since proved the generalization of this to implicit functions of several variables, G(z,w1,w2,...,w(N))=0. A good mathematician friend has scoured literature searches and come up with the usual papers on the Faa di Bruno formula and Lagrange Inversion Formula, which of course are all closely related to what I have done, but not exactly (and, of course, in mathematics, exactly counts for everything).
I have no access to math journal subscriptions. I have gotten what I can through Google searches, the Wolfram MathWorld site, and through my local county library online. Based upon what my mathematician friend (who DOES have access to university libraries and such) and the searches I have done - and the fact that the peer-reviewed journal to which I submitted my formula has not contacted me since I submitted my paper there in April 2010 to tell me that others have done the same - I am fairly confident that nobody else has come up with the same formula that I have (at least not published it).
But, I want to ask YOU all, here at MaplePrimes, if you know of anyone who has come up with the general formula, even if it's part of a computer algebra system such as Maple. So, it should be just a simple yes/no answer.
I am NOT asking you to solve this problem for me.
I'll have to say that I am surprised how many proofs of the same result, the same theorem, or the same formula, I have seen in published works, such as of the Faa da Bruno and LI formulae. Not that that is a bad thing. It is good to have different proofs. Just as long as *I* am given the same chance to publish an unoriginal result.
I sort of need to know this because I am building upon and generalizing this work and am using it to do other things in math and in chemical engineering.