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{ \bf Dick Askey: A Special (and VERY IMPORTANT!) Guru Indeed }
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{\it Doron ZEILBERGER}
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Special Functions are functions that occur so often that  they deserve a name,
but even more important than functions are {\it people}, and Dick Askey is one
of the most special people I have ever met.


In this brief note, let me mention a small sample of the very significant mathematics that he inspired.

$\bullet$ It was Dick who challenged Dominique Foata to find a combinatorial proof of the Mehler formula, and that
lead to Foata's beautiful combinatorial approach to Special Functions, pursued by him, his collaborators, and
many others.

$\bullet$ It was Dick who had brilliant PhD students, including Dennis Stanton, that became the
absolute unit of quality for all PhD students.  Being $x$-Dennis with $x>\frac{1}{2}$ means
that the student is very good. Of course $x \leq 1$, and the inequality is {\it sharp}, 
with only one case (guess who?) achieving $x=1$.

$\bullet$ Dick is very passionate about mathematics education, something very rate amongst research mathematicians, and
is a `gadfly' (with co-gadfly George Andrews) about what they deemed misguided reforms in K-12 education, stating
that {\it Good intentions are not enough}. Dick did not just criticize, but set an example by writing
insightful articles for the {\it Mathematics Teacher}, the leading periodical for high-school teachers,
about Fibonacci and Lucas numbers.

$\bullet$ The `Askey scheme' (aka {\it tableau d'Askey}), hanging in my office (nicely designed by Jacques Labelle), was
the {\bf conceptual skeleton} of lots of great research in special functions, highlighting the
Askey hypergeometric hierarchy, with the Racah and Askey-Wilson polynomials on the top.

$\bullet$ Dick caught the $q$-disease, and along with George Andrews and others (Mizan Rahman, George Gasper,
Dennis Stanton, Frank Garvan to name a few) inspired lots of insightful {\it $q$-analogs} of classical
theorems, that lead to insightful combinatorial interpretations (Xavier Viennot and his school, Bill Chen and his school, and many others).

$\bullet$ The {\it Askey-Gasper inequality} was the {\bf crucial fact} needed in the proof of one
of the most {\it important} open problems of the $20$-th century, Louis de Branges' proof of the Bieberbach conjecture.

Finally, let me mention Dick's influence on myself.

$\bullet$ Dick was a  great professional father-figure. He is the one who challenged me to prove
George Andrews' $q$-Dyson conjecture, that I did, in 1983 (published in 1985) in collaboration with Dave Bressoud.
He is the one who challenged me to prove the $G_2$ case of Ian Macdonald's Constant Term Conjecture (that I did, also done independently by Laurent Habsieger),
where I used the Dixon identity, that I learned from him and from Foata.
Dick also challenged me to prove the $G_2$-dual case of the same conjecture, that I did using what I called the
{\it Stembridge-Stanton} trick. That method was later  used by another whiz, Frank Garvan, to prove the $F_4$ case.

$\bullet$ Dick  was an implicit, but very strong, influence in the development of so-called {\bf Wilf-Zeilberger algorithmic proof theory}.


{\bf Thank you Dick!}


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Doron Zeilberger, Department of Mathematics, Rutgers University (New Brunswick), Hill Center-Busch Campus, 110 Frelinghuysen
Rd., Piscataway, NJ 08854-8019, USA. \hfill\break
Email: {\tt DoronZeil at gmail  dot com}   \quad .



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