A combinatorial interpretation for the Schett recurrence on the Jacobian elliptic functions

Author:
Dominique Dumont

Journal:
Math. Comp. **33** (1979), 1293-1297

MSC:
Primary 33A25; Secondary 05A15

DOI:
https://doi.org/10.1090/S0025-5718-1979-0537974-1

MathSciNet review:
537974

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Abstract | References | Similar Articles | Additional Information

Abstract: The coefficients introduced by Alois Schett containing the Taylor series expansions of the Jacobian elliptic functions are proved to count certain classes of permutations.

**[1]**D. ANDRE, "Développement de et ," C. R. Acad. Sci. Paris, v. 88, 1879, pp. 965-967.**[2]**D. FOATA & M. P. SCHÜTZENBERGER,*Théorie Géométrique des Polynômes Eulériens*, Lecture Notes in Math., Vol. 138, Springer-Verlag, Berlin and New York, 1970.**[3]**A. SCHETT, "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions,"*Math. Comp.*, v. 30, 1976, pp. 143-147. MR**0391477 (52:12298)****[4]**A. SCHETT, Addendum to "Properties of the Taylor series expansion coefficients of the Jacobian elliptic functions,"*Math. Comp.*, v. 31, 1977, Microfiche supplement.**[5]**A. SCHETT, "Recurrence formula of the Taylor series expansion coefficients of the Jacobian elliptic functions,"*Math. Comp.*, v. 31, 1977, pp. 1003-1005. MR**0442301 (56:687)****[6]**G. VIENNOT, "Une interprétation combinatoire des coefficients des développements en série entière des fonctions elliptiques de Jacobi,"*J. Combinatorial Theory*. (To appear.) MR**583951 (81h:33003)**

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DOI:
https://doi.org/10.1090/S0025-5718-1979-0537974-1

Article copyright:
© Copyright 1979
American Mathematical Society