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Polynomials biorthogonal to Appell's polynomials

  • Edward D. Fackerell (a1) and R.A. Littler (a2)

Abstract

We present the solution of a long-standing problem, namely, the determination of a set of polynomials in two independent variables which are biorthogonal over a triangular region to a set of polynomials previously introduced by Appell. Some elementary properties of our polynomials are investigated.

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References

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[1]Appell, , “Sur les séries hypergéométriques de deux variables, et sur des équations différentielles linéaires aux dérivées partielles”, C.R. Aoad. Sci. Paris 90 (1860), 296299.
[2]Appell, , “Sur les séries hypergéometriques de deux variables, et sur des équations différentielles linéaires simultanées aux dérivées partielles”, C.R. Aoad. Sci. Paris 90 (1860), 731–731.
[3]Appell, P., “Sur des polynômes de deux variables analogues aux polynômes de Jacobi”, Arch. Math. Phys. 66 (1881), 238245.
[4]Appell, , “Sur les fonctions hypergéométriques de deux variables”, J. Math. Pures Appl. (3) 8 (1882), 173216.
[5]Appell, P., Kampé de Fériet, J., Fonctions hypergéométriques et hypersphériques. Polynomes d'Hermite (Gauthier-Villars, Paris, 1926).
[6]Courant, R. and Hilbert, D., Methods of mathematical physics, Volume 1 (Interscience, New York, 1953).
[7]Erdélyi, Arthur, Magnus, Wilhelm, Oberhettinger, Fritz, Tricomi, Francesco G. (edited by), Higher transcendental functions, Volume I. Based, in part, on notes left by Harry Bateman. (McGraw-Hill, New York, Toronto, London, 1953.)
[7]Erdélyi, Arthur, Magnus, Wilhelm, Oberhettinger, Fritz, Tricomi, Francesco G. (edited by), Higher transcendental functions, Volume II. Based, in part, on notes left by Harry Bateman. (McGraw-Hill, New York, Toronto, London, 1953.)
[9]Karlin, Samuel and McGregor, James, “On some stochastic models in genetics”, Stochastic models in medicine and biology, 245279 (Proc. Sympos. University of Wisconsin, Madison, June 1963. University of Wisconsin Press, Madison, 1964).
[10]Kimura, Motoo, “Random genetic. drift in a tri-allelic locus; exact solution with a continuous model”, Biometrics 12 (1956), 5766.
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Polynomials biorthogonal to Appell's polynomials

  • Edward D. Fackerell (a1) and R.A. Littler (a2)

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