Geodesic
On \(q\)-interpolation formulae and their applications
Electronic transactions on numerical analysis, Tome 45 (2016), pp. 58-74
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
Classification : 65D05, 65D30, 41A05, 41A55
Keywords: $q$-Taylor series, Jackson's $q$-difference operator, Newton interpolation formulae, $q$-quadrature rules of weighted interpolatory type 
@article{ETNA_2016__45__a22,
     author = {Eslahchi,  M.R. and Masjed-Jamei,  Mohammad},
     title = {On \(q\)-interpolation formulae and their applications},
     journal = {Electronic transactions on numerical analysis},
     pages = {58--74},
     year = {2016},
     volume = {45},
     zbl = {1338.65027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2016__45__a22/}
}
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Eslahchi,  M.R.; Masjed-Jamei,  Mohammad. On \(q\)-interpolation formulae and their applications. Electronic transactions on numerical analysis, Tome 45 (2016), pp. 58-74. http://geodesic.mathdoc.fr/item/ETNA_2016__45__a22/