Comptes Rendus
Combinatorics/Ordinary differential equations
Correlation between Adomian and partial exponential Bell polynomials
[Corrélation des polynômes d'Adomian et des polynômes de Bell exponentiels partiels]
Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 929-936.

Nous montrons des relations de récurrence entre les vecteurs partition des polynômes de Bell exponentiels partiels. Utilisant ces relations, le n-ième polynôme d'Adomian, pour n'importe quel opérateur non linéaire, s'exprime explicitement en termes des polynômes de Bell exponentiels partiels. On en déduit des identités nouvelles pour ces derniers, via la solution de certaines équations différentielles ordinaires, en utilisant la méthode de décomposition d'Adomian.

We obtain some recurrence relationships among the partition vectors of the partial exponential Bell polynomials. On using such results, the n-th Adomian polynomial for any nonlinear operator can be expressed explicitly in terms of the partial exponential Bell polynomials. Some new identities for the partial exponential Bell polynomials are obtained by solving certain ordinary differential equations using the Adomian decomposition method.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.08.002

Kuldeep Kumar Kataria 1 ; Palaniappan Vellaisamy 1

1 Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
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Kuldeep Kumar Kataria; Palaniappan Vellaisamy. Correlation between Adomian and partial exponential Bell polynomials. Comptes Rendus. Mathématique, Volume 355 (2017) no. 9, pp. 929-936. doi : 10.1016/j.crma.2017.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.08.002/

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