A new type of Taylor series expansion

A new type of Taylor series expansion

We 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 speci...

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Veröffentlicht in:Journal of inequalities and applications 2018, Vol.2018 (1), p.116-10, Article 116
Hauptverfasser: Masjed-Jamei, Mohammad, Moalemi, Zahra, Area, Iván, Nieto, Juan J.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Applications of Mathematics
Assembly lines
Error analysis
Error bound
Generalized Taylor expansion
Integral remainder
Integration by parts
Jacobi and Laguerre polynomials
Mathematics
Mathematics and Statistics
Series expansion
Taylor series
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Beschreibung
Zusammenfassung:We 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.
ISSN:1025-5834
1029-242X
1029-242X
DOI:10.1186/s13660-018-1709-8