Geodesic
Recurrences and Legendre Transform
Séminaire lotharingien de combinatoire, Tome 29 (1992)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

A binomial identity which relates to the famous Apéry numbers and the sums of cubes of binomial coefficients (for which Franel has established a recurrence relation almost one hundred years ago) can be seen as a particular instance of a Legendre transform between sequences. A proof of this identity can be based on the more general fact that the Apéry and Franel recurrence relations themselves are conjugate via Legendre transform. This motivates a closer look at conjugacy of sequences satisfying linear recurrence relations with polynomial coefficients. The role of computer-aided proof and verification in the study of binomial identities and recurrence relations is illustrated, and potential applications of conjugacy in diophantine approximation are mentioned. 

@article{SLC_1992_29_a1,
     author = {Volker Strehl},
     title = {Recurrences and {Legendre} {Transform}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {29},
     year = {1992},
     url = {http://geodesic.mathdoc.fr/item/SLC_1992_29_a1/}
}
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AU  - Volker Strehl
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JO  - Séminaire lotharingien de combinatoire
PY  - 1992
VL  - 29
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1992_29_a1/
ID  - SLC_1992_29_a1
ER  - 
%0 Journal Article
%A Volker Strehl
%T Recurrences and Legendre Transform
%J Séminaire lotharingien de combinatoire
%D 1992
%V 29
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SLC_1992_29_a1/
%F SLC_1992_29_a1
Volker Strehl. Recurrences and Legendre Transform. Séminaire lotharingien de combinatoire, Tome 29 (1992). http://geodesic.mathdoc.fr/item/SLC_1992_29_a1/