## On q-interpolation formulae and their applications

M. R. Eslahchi and Mohammad Masjed-Jamei

### Abstract

It is shown that the q-Taylor series corresponding to Jackson's q-difference operator can be generated by the Newton interpolation formulae and the related remainders can be therefore written as the residue of a Newton interpolation formula. The advantage of this approach is that some constraints such as q-integrability in a domain and existence of the q-derivatives of $f$ at zero up to order n are no longer necessary. Two q-quadrature formulae of weighted interpolatory type are derived in this direction and some numerical examples for approximating definite quadratures and solving ordinary differential equations are then given

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### Key words

q-Taylor series, Jackson's q-difference operator, Newton interpolation formulae, q-quadrature rules of weighted interpolatory type

### AMS subject classifications

65D05, 65D30, 41A05, 41A55

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