On a q-analogue of Faà di Bruno's determinant formula

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: Keywords: Complete Bell polynomial Determinant Faà di Bruno's formula q-analogue a b s t r a c t Faà di Bruno's formula is the higher chain rule for differentiation. By means of Gessel's q-composition we derive a q-analogue of Faà di Bruno's determinant formula for the nth derivative of a composite function. The formula is regarded as a new form of the q-analogue of Faà di Bruno's formula. We also derive q-analogues of the complete Bell polynomials, which are in the form of a determinant. The q-complete Bell polynomials include the classical complete Bell polynomials as a special case.