Bell polynomials and differential equations of Freud-type polynomials
Mathematical and Computer Modelling: An International Journal
General identities on Bell polynomials
Computers & Mathematics with Applications
Some extensions of Faà di Bruno's formula with divided differences
Computers & Mathematics with Applications
Bell polynomials and generalized Blissard problems
Mathematical and Computer Modelling: An International Journal
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We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They arise considering the derivatives of functions f in several variables @f^(^i^), (i = 1, 2, ..., m), where @f^(^i^) are composite functions of different orders, i.e. @f^(^i^) (t) = ^(^i^,^1^) (^(^i^,^2^) (... (^(^i^,^r^"^i^) (t))), (i = 1, 2, ..., m). We show that these new polynomials are always expressible in terms of the ordinary Bell polynomials, by means of suitable recurrence relations or formal multinomial expansions. Moreover, we give a recurrence relation for their computation.