On Fejér's inequalities for the Legendre polynomials
Sign Up to like & getrecommendations! Published in 2017 at "Mathematische Nachrichten"
DOI: 10.1002/mana.201600461
Abstract: We present various inequalities for the sum Sn(t)=∑k=0nPk(t),where Pk denotes the Legendre polynomial of degree k. Among others we prove that the inequalities 25(1+t)≤Sn(t)and3−12(1−t2)≤Sn(t)hold for all n≥1 and t∈[−1,1]. The constant factors 2/5 and (3−1)/2… read more here.
Keywords: legendre polynomials; inequalities legendre; fej inequalities;
Numerical analysis of nonlinear variable fractional viscoelastic arch based on shifted Legendre polynomials
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7306
Abstract: An innovative numerical procedure for solving the viscoelastic arch problem based on variable fractional rheological models, directly in time domain, is proposed and investigated. First, the nonlinear integral‐differential governing equation is established according to the… read more here.
Keywords: arch; analysis; variable fractional; shifted legendre ... See more keywords
Solving uncertain differential equations using interval legendre polynomials based collocation method
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DOI: 10.1080/09720502.2019.1638614
Abstract: Abstract This paper proposes a new technique based on interval Legendre polynomials in the collocation method for solving n-the order uncertain boundary value problems. Firstly, the proposed method is illustrated by different example problems. Further,… read more here.
Keywords: method solving; method; interval legendre; legendre polynomials ... See more keywords
Evaluation of Legendre polynomials by a three-term recurrence in floating-point arithmetic
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DOI: 10.1093/imanum/dry079
Abstract: We prove new error estimates for a three-term recurrence that is used to compute Legendre polynomials. To this end we derive a bilinear representation of the cross-product of Legendre functions and demonstrate estimates of the… read more here.
Keywords: three term; legendre polynomials; recurrence; term recurrence ... See more keywords
A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)
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DOI: 10.1186/s13662-020-02984-4
Abstract: Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to… read more here.
Keywords: model novel; numerical solution; novel coronavirus; alternative legendre ... See more keywords
Mechanical nature of a single walled carbon nanotube using Legendre’s polynomials
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Theoretical and Applied Mechanics"
DOI: 10.15632/jtam-pl.56.4.1153
Abstract: This paper is concerned with the mechanical response of a single-walled carbon nanotube. Euler-Bernoulli’s beam theory and Hamilton’s principle are employed to derive the set of governing differential equations. An efficient variational method is used… read more here.
Keywords: single walled; legendre polynomials; walled carbon; carbon nanotube ... See more keywords
Applications of the q-Derivative Operator to New Families of Bi-Univalent Functions Related to the Legendre Polynomials
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DOI: 10.3390/axioms11110595
Abstract: By using the q-derivative operator and the Legendre polynomials, some new subclasses of q-starlike functions and bi-univalent functions are introduced. Several coefficient estimates and Fekete–Szegö-type inequalities for functions in each of these subclasses are obtained.… read more here.
Keywords: univalent functions; derivative operator; legendre polynomials; operator new ... See more keywords