Masjed-Jamei, MohammadMoalemi, ZahraArea Carracedo, Iván CarlosNieto Roig, Juan José2019-10-262019-10-262018-05-15Masjed-Jamei, M., Moalemi, Z., Area, I., & Nieto, J. (2018). A new type of Taylor series expansion. Journal Of Inequalities And Applications, 2018(1). doi: 10.1186/s13660-018-1709-8http://hdl.handle.net/10347/19953We present a variant of the classical integration by parts to introduce a new type of Taylor series expansion and to present some closed forms for integrals involving Jacobi and Laguerre polynomials, which cannot be directly obtained by usual symbolic computation programs, i.e., only some very specific values can be computed by the mentioned programs. An error analysis is given in the sequel for the introduced expansion.eng© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were madehttp://creativecommons.org/licenses/by/4.0/Generalized Taylor expansionIntegration by partsIntegral remainderError boundJacobi and Laguerre polynomialsjournal article10.1186/s13660-018-1709-81029-242Xopen access