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Two almost Identical Papers

August 9, 2013

Years ago, when Issac Newton published his “Principia Mathematica“, no one has a doubt he is the creator of this all powerful, all important Calculus.  Today, in retrospect, many people think it was Leibneitz, a lesser German mathematician than Newton, who could have done it first.  And to be honest, his notation is more modern and more in line with what our undergraduates are using.

So?  “Who Invented calculus?” you might ask.  Most people who glorify Newton will have no doubt it’s that guy with the “apple” that dropped on his head.  But a few experts and historians prefer to give the honour to Gottfried Wilhelm von Leibniz who happened to be only four years younger than Sir Issac Newton.

Today, the title that who “first prove” this or who “first discovered” that is of utmost importance.  There will be argument and court cases before it is settled.  If the courts were established, Newton and Leibniz may be in there for a long while, longer than the OJ Simpson case.

And if two papers were exactly the same in contents, one will not be published, if found out.  The questions then will be, what if two schools of thoughts who seldom interact, published two material of similar content?  I happened to spend a lot of time in two different schools of thoughts on Special Functions.  One school of thought was born out of Al-Salam, Chihara and then Ismail, Zhang, Koorwinder etc who were mainly in Canada, USA and maybe Hong Kong.  The other school of thought, more algebraic, started with a few Europeans, namely J. C. Medem (Seville, Spain), R. Alvarez-Nodarse (Coimbra) and F. Marcellán (Madrid).

One paper, born out of this Indian mathematican, Datta, and an American Griffin was hurriedly published in the Ramanujan Journal, a tiptop journal in math.  It was in such a hurry, it has more mistakes than a typical master thesis.  But this Datta -Griffin paper was quoted numerous times by the mathematical community.  Nobody even checked that work of Medem and others (some his students) were exact in content if not the same on the subject of the Hahn structure equations.  I have to admit, the European uses the Dual of the polynomial space and is more abstract (and elegant) while Datta and Griffin both churned out the result almost “by brute force”.

Later Ana Loureiro (Portuguese) and Pascal Maroni (French, who has published with Marcellán) also wrote an article regarding similar topic in 2011 Around q-Appell Poly. Seq. (click on this link and buy it for only forty dollars!)

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